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

0,3

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

Formula

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

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);

Crossrefs

Cf. A000073, A002002, A213684.

Sequence in context: A069030 A373281 A111993 * A113996 A340538 A062875

Adjacent sequences: A341263 A341264 A341265 * A341267 A341268 A341269

Keyword

nonn

Author

Alois P. Heinz, Feb 07 2021

Status

approved