A258473 Number of partitions of n into two sorts of parts having exactly 3 parts of the second sort.

1, 5, 16, 41, 91, 186, 351, 635, 1090, 1824, 2939, 4652, 7162, 10875, 16159, 23758, 34321, 49145, 69389, 97213, 134608, 185172, 252182, 341443, 458413, 612186, 811567, 1070826, 1403784, 1832370, 2378320, 3074642, 3954869, 5068684, 6466697, 8222640, 10412903

Offset

3,2

Links

Alois P. Heinz, Table of n, a(n) for n = 3..1000

Maple

b:= proc(n, i) option remember; series(`if`(n=0, 1,
      `if`(i<1, 0, add(b(n-i*j, i-1)*add(x^t*
       binomial(j, t), t=0..min(3, j)), j=0..n/i))), x, 4)
    end:
a:= n-> coeff(b(n$2), x, 3):
seq(a(n), n=3..40);

Mathematica

b[n_, i_] := b[n, i] = Series[If[n==0, 1, If[i<1, 0, Sum[b[n-i*j, i-1]*Sum[ x^t*Binomial[j, t], {t, 0, Min[3, j]}], {j, 0, n/i}]]], {x, 0, 4}];
a[n_] := Coefficient[b[n, n], x, 3];
a /@ Range[3, 40] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)

Crossrefs

Column k=3 of A256193.

Sequence in context: A081997 A078449 A257199 * A014161 A014166 A014171

Adjacent sequences: A258470 A258471 A258472 * A258474 A258475 A258476

Keyword

nonn

Author

Alois P. Heinz, May 31 2015

Status

approved