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
Keywords
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
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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
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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 *)
Comments