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 A307395 #27 Apr 24 2024 08:48:02
%S A307395 1,4,10,19,28,28,1,-80,-242,-485,-728,-728,1,2188,6562,13123,19684,
%T A307395 19684,1,-59048,-177146,-354293,-531440,-531440,1,1594324,4782970,
%U A307395 9565939,14348908,14348908,1,-43046720,-129140162,-258280325,-387420488,-387420488,1,1162261468
%N A307395 Expansion of 1/((1 - x) * ((1 - x)^3 + x^3)).
%H A307395 Seiichi Manyama, <a href="/A307395/b307395.txt">Table of n, a(n) for n = 0..4000</a>
%H A307395 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,3).
%F A307395 a(n) = Sum_{k=0..floor(n/3)} (-1)^k*binomial(n+3,3*k+3).
%F A307395 a(n) = 4*a(n-1) - 6*a(n-2) + 3*a(n-3) for n > 2.
%F A307395 a(6*n) = 1.
%F A307395 a(n) = 1 - A057681(n+3). - Yomna Bakr and _Greg Dresden_, Apr 22 2024
%t A307395 LinearRecurrence[{4, -6, 3}, {1, 4, 10}, 38] (* _Amiram Eldar_, May 13 2021 *)
%o A307395 (PARI) {a(n) = sum(k=0, n\3, (-1)^k*binomial(n+3, 3*k+3))}
%o A307395 (PARI) N=66; x='x+O('x^N); Vec(1/((1-x)*((1-x)^3+x^3)))
%Y A307395 Column 5 of A307394.
%Y A307395 Partial sums of A057083.
%K A307395 sign,easy
%O A307395 0,2
%A A307395 _Seiichi Manyama_, Apr 07 2019