
If you want to see a webbook with 16 exciting theorems about algebraic equations satisfied
by sequences enumerating onedimensinal walks with a given set of steps, for 16 different
choices of stepsets with steps of size at most 2
the input yields
the output

If you want to see a webbook with 32 exciting theorems about algebraic equations satisfied
by sequences enumerating onedimensinal walks with a given set of steps, for 32 different
choices of stepsets with steps of size at most 3
the input yields
the output
[16 of these theorems are already in the previous webbook]

If you want to see a webbook with 16 exciting theorems about linear recurrence equations
satisfied by sequences enumerating onedimensinal walks with a given set of steps, for 16 different
choices of stepsets with steps of size at most 2
the input yields
the output

If you want to see a webbook with 32 exciting theorems about linear recurrence equations
satisfied by sequences enumerating onedimensinal walks with a given set of steps, for 32 different
choices of stepsets with steps of size at most 3
the input yields
the output
[16 of these theorems are already in the previous webbook]

If you want to see the Asymptotic behavior of the random variable "final Location of a OneDimensional (LUCKY!)
Walker with Step Set, {1, 1}", or equivalently the amount of money a surviving gambler
at a fair casino (with a fair coin where you win a dollar with prob. 1/2 and lose with prob. 1/2),
the input yields
the output

If you want to see the Asymptotic behavior of the random variable "final Location of a OneDimensional (LUCKY!)
Walker with Step Set, {1,0, 1}", or equivalently the amount of money a surviving gambler
at a fair casino (with a fair die where you win a dollar with prob. 1/3 and lose with prob. 1/3, and nothing happens
with prob. 1/3)
the input yields
the output

If you want to see the Asymptotic behavior of the random variable "final Location of a OneDimensional (LUCKY!)
Walker with Step Set, {2,1, 1,2}", or equivalently the amount of money a surviving gambler
at a fair casino (with a fair die where you win two dollars with prob. 1/4, you win one dollar with prob. 1/4,
you lose two dollars with prob. 1/4, and you lose one dollar with prob. 1/4)
the input yields
the output

If you want to see the Asymptotic behavior of the random variable "final Location of a OneDimensional (LUCKY!)
Walker with Step Set, {2,1,0, 1,2}", or equivalently the amount of money a surviving gambler
at a fair casino (with a fair die where you win two dollar with prob. 1/5, you win one dollar with prob. 1/5,
you lose two dollars with prob. 1/5, you lose one dollar with prob. 1/5, and nothing happens with prob. 1/5)
the input yields
the output

If you want to see the Asymptotic behavior of the random variable "final Location of a OneDimensional (LUCKY!)
Walker with Step Set, {3,2,1, 1,2,3}", or equivalently the amount of money a surviving gambler
at a fair casino (with a fair die where you win three dollars with prob. 1/6, you win two dollars with prob. 1/6, you win one dollar with prob. 1/6,
you lose three dollars with prob. 1/6, you lose two dollars with prob. 1/6, and you lose one dollar with prob. 1/6)
the input yields
the output

If you want to see the Asymptotics of a Gambler's Chance of Ending with, 0, Dollars and never
being in debt after n rolls with a various choices of fair dice
the input yields
the output
[Note that the leading asymptotics is always of the form C*n^{3/2}, for some constant C]

If you want to see the Asymptotics of a Gambler's Chance of surviving without debt
n rolls with a various choices of fair dice
the input yields
the output
[Note that the leading asymptotics is always of the form C*n^{1/2}, for some constant C]

If you want to see a webbook with 16 exciting theorems about algebraic equations satisfied
by sequences enumerating onedimensinal walks with a given set of steps, for 16 different
choices of stepsets with steps of size at most 2, with SKETCHES OF PROOFS
the input yields
the output
[Note, that the theorems are the same as the above oW1D1,
but now we sketch proofs]

If you want to see
the MONSTER (20th order!) linear recurrence operator annihilating the enumerating sequence of nstep
walks with fundamental set of steps, {3, 1, 2}
that start and end at 0 and never venture to the left of 0 , followed by the 20 initial values (n=1 through n=20),
in Maple input notation is
the input yields
the output

If you want to see
the MONSTER (21st order!) linear recurrence operator annihilating the enumerating sequence of nstep
walks with fundamental set of steps, {3, 1, 2}
that start at 0 and never venture to the left of 0, and are allowed to end anywhere, followed by the 21 initial values (n=1 through n=20),
in Maple input notation is
the input yields
the output