A327552 Number of partitions in all twice partitions of n where the first partition is strict.

0, 1, 2, 7, 11, 29, 63, 125, 225, 489, 930, 1704, 3260, 5859, 10868, 20026, 35062, 61660, 111789, 191119, 337432, 585847, 1003876, 1705380, 2921394, 4930357, 8311554, 14013583, 23435178, 38849655, 64847870, 106784912, 175699558, 289676875, 472418418, 772944773

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..3200

Example

a(3) = 7 = 1+1+1+2+2 counting the partitions in 3, 21, 111, 2|1, 11|1.

Maple

b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
      `if`(n=0, [1, 0], b(n, i-1)+(p->p+[0, p[1]])(
      combinat[numbpart](i)*b(n-i, min(n-i, i-1)))))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=0..36);

Mathematica

b[n_, i_] := b[n, i] = If[i(i+1)/2<n, {0, 0}, If[n==0, {1, 0}, b[n, i-1] + Function[p, p + {0, p[[1]]}][PartitionsP[i] b[n-i, Min[n-i, i-1]]]]];
a[n_] := b[n, n][[2]];
a /@ Range[0, 36] (* Jean-François Alcover, Dec 17 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000009, A000041, A271619, A327607.

Sequence in context: A057025 A055469 A361151 * A336342 A284354 A228076

Adjacent sequences: A327549 A327550 A327551 * A327553 A327554 A327555

Keyword

nonn

Author

Alois P. Heinz, Sep 16 2019

Status

approved