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 A379824 #6 Jan 06 2025 06:56:12
%S A379824 1,-1,1,0,1,2,5,12,31,79,207,546,1457,3919,10621,28968,79459,219053,
%T A379824 606611,1686660,4706879,13178956,37012219,104235300,294301801,
%U A379824 832901237,2362328425,6713749632,19116443881,54526962682,155785926413,445772216816,1277394033603
%N A379824 a(n) = [x^n] 2 / (1 + x*(2*x + 3) + sqrt((x + 1)*(1 - 3*x))). Alternating row sums of A379907.
%F A379824 a(n) = (-1)^n * Sum_{k=0..n} hypergeom([k - n, k/2 + 1, k/2 + 1/2], [1, k + 2], 4).
%F A379824 a(n + 2) + a(n + 3) = A114589(n).
%p A379824 a := n -> (-1)^n*add(hypergeom([k-n, k/2+1, (k+1)/2], [1, k + 2], 4), k = 0..n):
%p A379824 seq(simplify(a(n)), n = 0..32);
%Y A379824 Cf. A379907, A114589.
%K A379824 sign
%O A379824 0,6
%A A379824 _Peter Luschny_, Jan 06 2025