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 A369849 #19 Mar 15 2024 07:25:15
%S A369849 1,2,3,4,6,13,35,92,220,484,1013,2092,4382,9404,20552,45185,99009,
%T A369849 215481,466361,1006897,2174834,4705895,10200142,22128873,48009456,
%U A369849 104111224,225655617,488945055,1059372394,2295532150,4974876116,10782658417,23371307904,50655960304
%N A369849 Number of compositions of 5*n-1 into parts 4 and 5.
%H A369849 Paolo Xausa, <a href="/A369849/b369849.txt">Table of n, a(n) for n = 1..1000</a>
%H A369849 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-4,1).
%F A369849 a(n) = A017827(5*n-1).
%F A369849 a(n) = Sum_{k=0..floor(n/4)} binomial(n+k,n-1-4*k).
%F A369849 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 4*a(n-4) + a(n-5).
%F A369849 G.f.: x*(1-x)^3/((1-x)^5 - x^4).
%t A369849 LinearRecurrence[{5, -10, 10, -4, 1}, {1, 2, 3, 4, 6}, 50] (* _Paolo Xausa_, Mar 15 2024 *)
%o A369849 (PARI) a(n) = sum(k=0, n\4, binomial(n+k, n-1-4*k));
%Y A369849 Cf. A099131, A368475, A369850, A369851.
%Y A369849 Cf. A017827.
%K A369849 nonn,easy
%O A369849 1,2
%A A369849 _Seiichi Manyama_, Feb 03 2024