By Andrew V. Sills and Doron Zeilberger
Last update of this webpage (but not article): April 17, 2012.
(previous updates of this page: March 13, 2012)
If you want to see the first 500 terms of the sequences C_{01j}(N) for j from 1 to 10,
both in exact rational arithmetic, and in floating-point,
the input
gives the output.
If you want to see the first 700 terms of the sequence C_{121}(N)
the input
gives the output.
If you want to conduct your own computer experiments with our data, we have
put all the 10 sequences C_{01j}(N) for 1 ≤ j ≤ 10, for
1 ≤ N ≤ 800, into one file, called
HANSC01,
in Maple readable format. We named that sequence C01r. For example,
C_{017}(597) could be gotten (once you uploaded that file),
by typing
C01r[7][597];
An even larger list then above,
put all the 10 sequences C_{01j}(N) for 1 ≤ j ≤ 10, for
1 ≤ N ≤ 850, into one file, called
HANSC01a,
in Maple readable format. We also named that sequence C01r. For example,
C_{017}(597) could be gotten (once you uploaded that file),
by typing
C01r[7][597];
If you want even more data, but in floating-point, we
put all the 40 sequences C_{01j}(N) for 1 ≤ j ≤ 40, for
1 ≤ N ≤ 1000, into one file, called
HANSC01f,
in Maple readable format. We named that sequence C01f. For example,
the floating-point approximation of
C_{017}(999) could be gotten gotten (once you uploaded that file),
by typing
C01f[7][999];
If you want to see
the 21 sequences C_{01(-j)}(N) for j from 0 to 20 and
1 ≤ N ≤ 500
the input
yields
the output ,
in Maple readable format. We named that sequence C01Minus.
To get C_{01(-j)}(N), simply type, C01Minus[j+1][N];
For example,
C_{01(-7)}(456) could be gotten (once you uploaded that file),
by typing
C01Minus[8][456];
If you want to see conjectured (appx.) asymptotic expressions for C_{01l}(N)
for l between 1 and 15,
the input
gives the output.
If you want to see the values, in floating-point, of C_{hkl}(N) for 0 < h < k < 10 , k ≥ 3, with gcd(h,k)=1 and
for l between 1 and 10, and N between 1 and 400
the input
gives the output.
If you want to see the first 1500 terms of the sequence C_{011}(N)*(2*N)!,
the input
gives the output.
[Added April 17, 2012]
If you want to see the first 2000 terms of the sequence C_{011}(N)*(2*N)!,
the input
gives the output.
If you want to see conjectured (appx.) asymptotic expressions for C_{011}(N)
(using 1500 terms rather than 900 as in oHANS10)
the input
gives the output.
[Added April 17, 2012]
If you want to see conjectured (appx.) asymptotic expressions for C_{011}(N)
(using 2000 terms rather than 1500 as in oHANS13)
the input
gives the output.
[Note the "shifting of the perihelion!", now the maxima are at 1(mod 32) and the minima at 17 (mod 32)]