This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A318947 #20 Mar 17 2025 05:44:35
%S A318947 0,0,0,0,1,6,26,97,331,1064,3277,9775,28448,81201,228211,633384,
%T A318947 1740037,4740327,12825008,34500649,92372683,246352952,654878173,
%U A318947 1736172895,4592568896,12125944161,31967715811,84170419272,221388694261,581807602839,1527909651152,4010192518105
%N A318947 Column 2 of triangle A318945.
%H A318947 Muniru A Asiru, <a href="/A318947/b318947.txt">Table of n, a(n) for n = 0..2000</a>
%H A318947 Czabarka, É., Flórez, R., Junes, L., & Ramírez, J. L., <a href="https://doi.org/10.1016/j.disc.2018.06.032">Enumerations of peaks and valleys on non-decreasing Dyck paths</a>, Discrete Mathematics (2018), 341(10), 2789-2807.
%F A318947 Let alpha(n) = Sum_{k=0..n} binomial(2*n-1-k,k-1)*hypergeom([2,2,1-k], [1,1-2*k+2*n], -1) then alpha(n) = a(n+3) for n >= 0. - _Peter Luschny_, Oct 28 2018
%F A318947 Conjectures from _Colin Barker_, Oct 28 2018: (Start)
%F A318947 G.f.: x^4*(1 - x)^3 / ((1 - 2*x)^3*(1 - 3*x + x^2)).
%F A318947 a(n) = 9*a(n-1) - 31*a(n-2) + 50*a(n-3) - 36*a(n-4) + 8*a(n-5) for n>7. (End)
%p A318947 a := n -> `if`(n < 3, 0, combinat:-fibonacci(2*n) - (n^2 + 9*n + 28)*2^(n - 6)):
%p A318947 seq(a(n), n=0..31); # _Peter Luschny_, Oct 28 2018
%o A318947 (GAP) Concatenation([0,0,0],List([3..31],n->Fibonacci(2*n)-(n^2+9*n+28)*2^(n-6))); # _Muniru A Asiru_, Oct 28 2018
%Y A318947 Cf. A318945.
%K A318947 nonn
%O A318947 0,6
%A A318947 _N. J. A. Sloane_, Sep 18 2018
%E A318947 More terms from _Peter Luschny_, Oct 28 2018
%E A318947 a(30) corrected by _Muniru A Asiru_, Oct 28 2018