A202192 Number of partitions of 5n with equal number of parts congruent to each of 1, 2, 3 and 4 modulo 5.

1, 1, 3, 8, 22, 53, 124, 269, 568, 1152, 2284, 4410, 8363, 15542, 28438, 51201, 90930, 159300, 275740, 471706, 798388, 1337478, 2219395, 3649432, 5950078, 9622364, 15442269, 24600952, 38919910, 61164114, 95513618, 148247892, 228761668, 351032568, 535772894

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..100

Index and properties of sequences related to partitions of 5n

Formula

a(n) = A046776(n) + A202086(n) + A202088(n).

a(n) = A046787(n) + A000041(n).

Mathematica

mkl[i_, l_] := Module[{ll, mn, x}, ll = If[Mod[i, 5] == 0, l, MapAt[#+1&, l, Mod[i, 5]]]; mn = Min[l] - 1; If[mn <= 0, ll, Map[# - mn&, ll]]];
g[n_, i_, t_] := g[n, i, t] = Module[{m, mx}, If[n < 0, 0, If[n == 0, If[ t[[1]] > 0 && Equal @@ t[[1 ;; 4]], 1, 0] , If[i == 0, 0, If[i < 5, mx = Max[t]; m = n - 10 mx + t[[1]] + 2 t[[2]] + 3 t[[3]] + 4 t[[4]]; If[m >= 0 && Mod[m, 10] == 0, 1, 0], g[n, i-1, t] + g[n-i, i, mkl[i, t]]]]]]];
a[n_] :=  g[5n, 5n, {0, 0, 0, 0}] + PartitionsP[n];
Table[a[n], {n, 0, 34}] (* Jean-François Alcover, May 25 2019, after Alois P. Heinz in A046787 *)

Crossrefs

Cf. A046776.

Sequence in context: A178525 A266187 A328002 * A027211 A027235 A086596

Adjacent sequences: A202189 A202190 A202191 * A202193 A202194 A202195

Keyword

nonn

Author

Max Alekseyev, Dec 14 2011

Extensions

a(33)-a(34) from Alois P. Heinz, May 24 2019

Status

approved