ez:=proc(): print(` NZx(x,d), NZ(d), NoamZ(d) `): end: read `W1D.txt`: NZx:=proc(x,d) local gu,z,i,gu1,gu2: gu:=z: gu1:=x+z*(gu-subs(x=0,gu))^2+z*diff(gu,x): gu1:=add(coeff(gu1,z,i)*z^i,i=0..2*d+2): while gu<>gu1 do gu2:=expand(x+z*(gu1-subs(x=0,gu1))^2+z*diff(gu1,x)): gu2:=add(coeff(gu2,z,i)*z^i,i=0..2*d+2): gu:=gu1: gu1:=gu2: od: [seq(coeff(gu1,z,2*i+1),i=0..d)]: end: NZ:=proc(d) local x,gu: gu:=NZx(x,d): subs(x=0,[seq(coeff(gu1,z,2*i+1),i=0..d)]): end: NoamZ:=proc(d) local gu,ope,eq,z,lu,vu,P,i,N, n,lu1: gu:=NZ(d): print(`The first `, d+1, `terms in Noam Zeilberger's sequence counting closed indecomposable linear lambda terms, as well as`): print(`closed bridgeless rooted trivalent maps (on oriented surfaces of arbitrary genus) are `): lprint(gu): ope:=Findrec(gu,n,N,14): if ope=FAIL then print(`no recurrence with ploynomial coefficients was found, we need more terms, or may be there is none`): else print(`a recurrence is`): lprint(ope): fi: eq:=Empir(gu,z,P): if eq=FAIL then print(`no algebraic equation was found, we need more terms, or may be there is none`): else print(`an algebraic equation is`): lprint(ope): fi: print(`Dividing the sequence by n! we get the new sequence `): lu:=[seq(gu[i]/(i-1)!,i=1..nops(gu))]: vu:=Zinn(lu): print(`A heuristic asymptotic is mu^n*n^theta , where`): print(`mu is approximately`, vu[2]): print(`and theta is approximately`, vu[1]): lu1:=[op(1..nops(lu)-2,lu)]: print(`To see how good it is ,the analogous values for the sequence with two less terms is`, Zinn(lu1)): end: