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

Author

Reinhard Zumkeller, May 07 2014

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Heegner Number
• Wikipedia, Heegner number

Crossrefs

Cf. A242217.

Programs

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

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 *)