OFFSET
0,2
COMMENTS
Both endpoints of each step have to satisfy the given restrictions.
a(n) is odd for n in {0, 2, 6, 14, 30, 62, ... } = { 2^n-2 | n>0 }.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..448
FORMULA
a(n) ~ exp(1)*(exp(1)-2) * n! * n. - Vaclav Kotesovec, Oct 13 2016
MAPLE
a:= proc(n) option remember; `if`(n<3, [1, 2, 7][n+1],
((n^3+10*n^2-10*n+1)*a(n-1)-(2*(4*n^3+2*n^2-29*n+28))
*a(n-2)+(4*(n-2))*(2*n-3)^2*a(n-3))/(n*(n+1)))
end:
seq(a(n), n=0..25);
MATHEMATICA
a[n_] := a[n] = If[n<3, {1, 2, 7}[[n+1]], ((n^3+10*n^2-10*n+1)*a[n-1] - (2*(4*n^3+2*n^2-29*n+28))*a[n-2] + (4*(n-2))*(2*n-3)^2*a[n-3])/(n*(n+1)) ]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jan 25 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Alois P. Heinz, Oct 10 2016
STATUS
approved