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A243229 Number of isoscent sequences of length n with exactly three ascents.

%I A243229 #16 Aug 27 2021 08:52:21
%S A243229 17,229,1819,11172,58847,280158,1242859,5238042,21245548,83685745,
%T A243229 322225735,1218705577,4544214608,16751906196,61188410692,221832968059,
%U A243229 799344529621,2865983103387,10233713828145,36419029944617,129245774064864,457623216922119
%N A243229 Number of isoscent sequences of length n with exactly three ascents.
%H A243229 Joerg Arndt and Alois P. Heinz, <a href="/A243229/b243229.txt">Table of n, a(n) for n = 6..100</a>
%F A243229 G.f.: x^6*(17 - 213*x + 1118*x^2 - 3135*x^3 + 4851*x^4 - 3492*x^5 - 262*x^6 + 1707*x^7 + 82*x^8 - 1050*x^9 + 189*x^10 + 297*x^11 - 122*x^12 + 11*x^13 + 3*x^14) / ((1 - x)^4*(1 - 2*x)^3*(1 - 4*x + 3*x^2 + x^3)^2*(1 - 8*x + 21*x^2 - 18*x^3 - 3*x^4 + 5*x^5 + 3*x^6)) (conjectured). - _Colin Barker_, May 04 2019
%p A243229 b:= proc(n, i, t) option remember; `if`(n<1, 1, expand(add(
%p A243229       `if`(j>i, x, 1) *b(n-1, j, t+`if`(j=i, 1, 0)), j=0..t+1)))
%p A243229     end:
%p A243229 a:= n-> coeff(b(n-1, 0$2), x, 3):
%p A243229 seq(a(n), n=6..35);
%t A243229 b[n_, i_, t_] := b[n, i, t] = If[n < 1, 1, Expand[Sum[
%t A243229     If[j>i, x, 1] *b[n-1, j, t + If[j == i, 1, 0]], {j, 0, t+1}]]];
%t A243229 a[n_] := Coefficient[b[n - 1, 0, 0], x, 3];
%t A243229 Table[a[n], {n, 6, 35}] (* _Jean-François Alcover_, Aug 27 2021, after Maple code *)
%Y A243229 Column k=3 of A242351.
%K A243229 nonn
%O A243229 6,1
%A A243229 _Joerg Arndt_ and _Alois P. Heinz_, Jun 01 2014