cp's OEIS Frontend

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

%I A341266 #16 Jul 21 2021 22:50:18
%S A341266 1,1,5,25,125,646,3395,18054,96885,523600,2845700,15537457,85160387,
%T A341266 468279280,2582140370,14272523740,79056303957,438711518556,
%U A341266 2438587839980,13574970187300,75668677723100,422294150816010,2359326605275755,13194525668986350,73857744668632275
%N A341266 a(n) is the n-th term of the n-fold self-convolution of the twice left-shifted tribonacci sequence (A000073).
%C A341266 The twice left-shifted tribonacci sequence begins: 1, 1, 2, 4, 7, 13, 24, ... .
%H A341266 Alois P. Heinz, <a href="/A341266/b341266.txt">Table of n, a(n) for n = 0..1323</a>
%F A341266 a(n) = [x^n] (1/(1-x-x^2-x^3))^n.
%p A341266 a:= n-> coeff(series((1/(1-x-x^2-x^3))^n, x, n+1), x, n):
%p A341266 seq(a(n), n=0..25);
%p A341266 # second Maple program:
%p A341266 g:= proc(n) g(n):= `if`(n<2, (n+1)*(2-n)/2, add(g(n-j), j=1..3)) end:
%p A341266 b:= proc(n, k) option remember; `if`(k<2, g(n),
%p A341266       (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
%p A341266     end:
%p A341266 a:= n-> b(n$2):
%p A341266 seq(a(n), n=0..25);
%Y A341266 Cf. A000073, A002002, A213684.
%K A341266 nonn
%O A341266 0,3
%A A341266 _Alois P. Heinz_, Feb 07 2021