OFFSET
3,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 3..1000
FORMULA
a(n) ~ c * 3^n, where c = 6.846206073498521357898163368676070142316815386135993166380819930419737... - Vaclav Kotesovec, Oct 11 2017
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1, k)+`if`(i>n, 0, b(n-i, i, k)*binomial(i+k-1, k-1))))
end:
a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k))(3):
seq(a(n), n=3..30);
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k] + If[i > n, 0, b[n - i, i, k] Binomial[i + k - 1, k - 1]]]];
a[n_] := With[{k = 3}, Sum[b[n, n, k - i] (-1)^i Binomial[k, i], {i, 0, k}]];
a /@ Range[3, 30] (* Jean-François Alcover, Dec 08 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 07 2017
STATUS
approved