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A202192 Number of partitions of 5n with equal number of parts congruent to each of 1, 2, 3 and 4 modulo 5. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified June 19 00:37 EDT 2021. Contains 345125 sequences. (Running on oeis4.)