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 A369804 #22 Feb 14 2024 06:10:09
%S A369804 1,0,0,1,5,15,36,80,181,431,1060,2617,6401,15521,37513,90741,219918,
%T A369804 533619,1295022,3141826,7619870,18478155,44810670,108676262,263576791,
%U A369804 639267800,1550434777,3760269946,9119740067,22118021213,53642768716,130099857234,315531401964
%N A369804 Expansion of 1/(1 - x^3/(1-x)^5).
%C A369804 Number of compositions of 5*n-3 into parts 3 and 5.
%H A369804 Seiichi Manyama, <a href="/A369804/b369804.txt">Table of n, a(n) for n = 0..1000</a>
%H A369804 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,11,-5,1).
%F A369804 a(n) = A052920(5*n-3) for n > 0.
%F A369804 a(n) = 5*a(n-1) - 10*a(n-2) + 11*a(n-3) - 5*a(n-4) + a(n-5) for n > 5.
%F A369804 a(n) = Sum_{k=0..floor(n/3)} binomial(n-1+2*k,n-3*k).
%F A369804 a(n) = A369845(n) - A369845(n-1). - _R. J. Mathar_, Feb 14 2024
%o A369804 (PARI) my(N=40, x='x+O('x^N)); Vec(1/(1-x^3/(1-x)^5))
%o A369804 (PARI) a(n) = sum(k=0, n\3, binomial(n-1+2*k, n-3*k));
%Y A369804 Cf. A079675, A368475, A369803.
%Y A369804 Cf. A369845, A369846, A369847, A369848.
%Y A369804 Cf. A052920.
%K A369804 nonn,easy
%O A369804 0,5
%A A369804 _Seiichi Manyama_, Feb 01 2024