A327590 Number of partitions in all twice partitions of n.

0, 1, 4, 10, 29, 63, 164, 339, 797, 1640, 3578, 7139, 15210, 29621, 60381, 117116, 232523, 442388, 863069, 1621560, 3105993, 5785525, 10894394, 20083143, 37434186, 68344449, 125774280, 228088127, 415668548, 747660318, 1351364816, 2413792653, 4327245170

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2000

Example

a(3) = 10 = 1+1+1+2+2+3 counting the partitions in 3, 21, 111, 2|1, 11|1, 1|1|1.

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, 0, b(n, i-1)+
      (p-> p+[0, p[1]])(combinat[numbpart](i)*b(n-i, min(n-i, i)))))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=0..42);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i<1, {0, 0}, b[n, i-1] + Function[p, p + {0, p[[1]]}][PartitionsP[i] b[n-i, Min[n-i, i]]]]];
a[n_] := b[n, n][[2]];
a /@ Range[0, 42] (* Jean-François Alcover, Dec 16 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000041, A006128, A063834, A066633, A327552, A327553, A327554, A327594.

Sequence in context: A164361 A006907 A305204 * A321344 A329156 A052946

Adjacent sequences: A327587 A327588 A327589 * A327591 A327592 A327593

Keyword

nonn

Author

Alois P. Heinz, Sep 17 2019

Status

approved