OFFSET
0,3
COMMENTS
a(n) is the number of n-step closed walks (from origin to origin) in 4-dimensional lattice where each step changes at most one component by -1 or by +1. - Alois P. Heinz, Oct 26 2019
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1054
FORMULA
From Vaclav Kotesovec, Oct 26 2019: (Start)
Recurrence: n^4*a(n) = (5*n^4 - 10*n^3 + 10*n^2 - 5*n + 1)*a(n-1) + (n-1)^2*(70*n^2 - 140*n + 113)*a(n-2) - (n-2)*(n-1)*(230*n^2 - 690*n + 583)*a(n-3) - 789*(n-3)*(n-2)^2*(n-1)*a(n-4) + 945*(n-4)*(n-3)*(n-2)*(n-1)*a(n-5).
a(n) ~ 9^(n+2) / (16 * Pi^2 * n^2). (End)
E.g.f.: exp(x) * BesselI(0,2*x)^4. - Ilya Gutkovskiy, Oct 26 2019
PROG
(PARI) {a(n) = polcoef(polcoef(polcoef(polcoef((1+w+x+y+z+1/w+1/x+1/y+1/z)^n, 0), 0), 0), 0)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 26 2019
EXTENSIONS
a(19)-a(22) from Alois P. Heinz, Oct 26 2019
STATUS
approved