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 A046776 #30 Sep 16 2019 18:12:38
%S A046776 1,0,0,1,5,15,36,75,146,271,495,891,1601,2851,5051,8851,15362,26331,
%T A046776 44642,74787,123991,203433,330717,532872,851779,1351147,2128324,
%U A046776 3330059,5177768,8002170,12296754,18791945,28566751,43204575,65022987,97395386,145217908
%N A046776 Number of partitions of 5n with equal number of parts congruent to each of 0, 1, 2, 3 and 4 (mod 5).
%C A046776 Number of partitions of m with equal numbers of parts congruent to each of 1, 2, 3 and 4 (mod 5) is 0 unless m == 0 mod 5.
%H A046776 Andrew Howroyd, <a href="/A046776/b046776.txt">Table of n, a(n) for n = 0..1000</a>
%H A046776 <a href="/wiki/Partitions_of_5n">Index and properties of sequences related to partitions of 5n</a>
%F A046776 a(n) = A202085(n) - A202086(n).
%F A046776 a(n) = A036884(n) - A036886(n).
%F A046776 a(n) = A036889(n) - A036892(n).
%F A046776 a(n) = A202087(n) - A202088(n).
%F A046776 G.f.: Sum_{k>=0} x^(3*k)/(Product_{j=1..k} 1 - x^j)^5. - _Andrew Howroyd_, Sep 16 2019
%p A046776 mkl:= proc(i,l) local ll, mn, ii, x; ii:= irem(i,5); ii:= `if`(ii=0, 5, ii); ll:= applyop(x->x+1, ii, l); mn:= min(l[]); `if`(mn=0, ll, map (x->x-mn, ll)) end:
%p A046776 g:= proc(n,i,t) local m, mx, j; if n<0 then 0 elif n=0 then `if`(nops ({t[]})=1, 1, 0) elif i=0 then 0 elif i<6 then mx:= max (t[]); m:= n-15*mx +add(t[j]*j, j=1..5); g(n,i,t):= `if`(m>=0 and irem(m, 15)=0, 1, 0) else g(n,i,t):= g(n, i-1, t) + g(n-i, i, mkl(i, t)) fi end:
%p A046776 a:= n-> g(5*n, 5*n, [0$5]):
%p A046776 seq(a(n), n=0..20); # _Alois P. Heinz_, Jul 04 2009
%t A046776 $RecursionLimit = 1000; mkl[i_, l_List] := Module[{ ll, mn, ii, x}, ii = Mod[i, 5]; ii = If[ii == 0, 5, ii]; ll = MapAt[#+1&, l, ii]; mn = Min[l]; If[mn == 0, ll, Map [#-mn&, ll]]]; g[n_, i_, t_List] := g[n, i, t] = Module[{ m, mx, j}, Which[n<0, 0 , n == 0, If[Length[t // Union] == 1, 1, 0], i==0, 0, i<6, mx = Max[t]; m = n-15*mx + Sum[t[[j]]*j, {j, 1, 5}]; If[m >= 0 && Mod[m, 15] == 0, 1, 0], True, g[n, i-1, t] + g[n-i, i, mkl[i, t]]]]; a[n_] := g[5*n, 5*n, {0, 0, 0, 0, 0}]; Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Jul 21 2015, after _Alois P. Heinz_ *)
%o A046776 (PARI) seq(n)={Vec(sum(k=0, n\3, x^(3*k)/prod(j=1, k, 1 - x^j + O(x*x^n))^5) + O(x*x^n))} \\ _Andrew Howroyd_, Sep 16 2019
%Y A046776 Cf. A046765, A046787.
%K A046776 nonn
%O A046776 0,5
%A A046776 _David W. Wilson_
%E A046776 a(18)-a(35) from _Alois P. Heinz_, Jul 04 2009
%E A046776 Edited by _Max Alekseyev_, Dec 11 2011
%E A046776 a(36) from _Alois P. Heinz_, Feb 03 2013