A242216 Number of partitions of n into Heegner numbers, cf. A003173.

1, 1, 2, 3, 4, 5, 7, 9, 11, 14, 17, 21, 25, 30, 36, 42, 49, 57, 66, 76, 87, 100, 114, 129, 146, 165, 185, 207, 232, 258, 287, 318, 352, 389, 428, 471, 517, 566, 619, 676, 737, 802, 872, 947, 1027, 1112, 1203, 1300, 1402, 1512, 1628, 1751, 1882, 2020, 2167, 2322

Offset

0,3

Comments

Heegner numbers = A003173(1..9) = {1,2,3,7,11,19,43,67,163}.

Links

Table of n, a(n) for n=0..55.

Eric Weisstein's World of Mathematics, Heegner Number

Wikipedia, Heegner number

Example

a(10) = #{7+3, 7+2+1, 7+1+1+1, 3+3+3+1, 3+3+2+2, 3+3+2+1+1, 3+3+4x1, 3+2+2+2+1, 3+2+2+1+1+1, 3+2+5x1, 3+7x1, 5x2, 4x2+1+1, 2+2+2+4x1, 2+2+6x1, 2+8x1, 10x1} = 17;
a(11) = #{11, 7+3+1, 7+2+2, 7+2+1+1, 7+4x1, 3+3+3+2, 3+3+3+1+1, 3+3+2+2+1, 3+3+2+1+1+1, 3+3+5x1, 3+4x2, 3+2+2+2+1+1, 3+2+2+4x1, 3+2+6x1, 3+8x1, 5x2+1, 4x2+1+1+1,2+2+2+5x1, 2+2+7x1, 2+9x1, 11x1} = 21;
a(12) = #{11+1, 7+3+2, 7+3+1+1, 7+2+2+1, 7+2+1+1+1, 7+5*1, 3+3+3+3, 3+3+3+2+1, 3+3+3+1+1+1, 3+3+2+2+2, 3+3+2+2+1+1, 3+3+2+4x1, 3+3+6x1, 3+4x2+1, 3+2+2+2+1+1+1, 3+2+2+5x1, 3+2+7x1, 3+9x1, 6x2, 5x2+1+1, 4x2+4x1, 2+2+2+6x1, 2+2+8x1, 2+10x1, 12x1} = 25.

Mathematica

heegnerNums = {1, 2, 3, 7, 11, 19, 43, 67, 163};
a[n_] := Length @ IntegerPartitions[n, All, heegnerNums];
Table[a[n], {n, 0, 55}] (* Jean-François Alcover, Jun 10 2019 *)

Prog

(Haskell)
a242216 = p [1, 2, 3, 7, 11, 19, 43, 67, 163] where
   p _          0 = 1
   p []         _ = 0
   p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
(Magma) [#RestrictedPartitions(n, {1, 2, 3, 7, 11, 19, 43, 67, 163}):n in [1..60]]; // Marius A. Burtea, Jun 10 2019

Crossrefs

Cf. A242217.

Sequence in context: A029001 A161306 A266744 * A111133 A279076 A076970

Adjacent sequences: A242213 A242214 A242215 * A242217 A242218 A242219

Keyword

nonn

Author

Reinhard Zumkeller, May 07 2014

Status

approved