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 A375169 #22 Jun 18 2025 16:16:44
%S A375169 1,2,3,4,6,11,22,43,80,144,257,462,839,1532,2798,5099,9274,16855,
%T A375169 30640,55728,101393,184490,335659,610628,1110790,2020635,3675822,
%U A375169 6686979,12164896,22130208,40258737,73237462,133231279,242370396,440913550,802098203,1459155634
%N A375169 Expansion of (1 - x) / ((1 - x)^3 - x^4).
%H A375169 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,1).
%F A375169 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4).
%F A375169 a(n) = Sum_{k=0..floor(n/4)} binomial(n+1-k,n-4*k).
%F A375169 a(n) = (n + 1)*hypergeom([(1-n)/4, (2-n)/4, (3-n)/4, -n/4], [2/3, 4/3, -1-n], -4^4/3^3). - _Stefano Spezia_, Jun 18 2025
%o A375169 (PARI) my(N=40, x='x+O('x^N)); Vec((1-x)/((1-x)^3-x^4))
%Y A375169 Cf. A024494, A052921, A124820, A137357.
%Y A375169 Cf. A003522, A107068.
%K A375169 nonn,easy
%O A375169 0,2
%A A375169 _Seiichi Manyama_, Aug 05 2024