A341266 a(n) is the n-th term of the n-fold self-convolution of the twice left-shifted tribonacci sequence (A000073).

1, 1, 5, 25, 125, 646, 3395, 18054, 96885, 523600, 2845700, 15537457, 85160387, 468279280, 2582140370, 14272523740, 79056303957, 438711518556, 2438587839980, 13574970187300, 75668677723100, 422294150816010, 2359326605275755, 13194525668986350, 73857744668632275

Offset: 0

Author

Alois P. Heinz, Feb 07 2021

Keywords

• nonn

Comments

The twice left-shifted tribonacci sequence begins: 1, 1, 2, 4, 7, 13, 24, ... .

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1323

Crossrefs

Cf. A000073, A002002, A213684.

Programs

Maple

a:= n-> coeff(series((1/(1-x-x^2-x^3))^n, x, n+1), x, n):
seq(a(n), n=0..25);
# second Maple program:
g:= proc(n) g(n):= `if`(n<2, (n+1)*(2-n)/2, add(g(n-j), j=1..3)) end:
b:= proc(n, k) option remember; `if`(k<2, g(n),
      (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);

Formula

a(n) = [x^n] (1/(1-x-x^2-x^3))^n.