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

%I A242216 #12 Feb 16 2025 08:33:22
%S A242216 1,1,2,3,4,5,7,9,11,14,17,21,25,30,36,42,49,57,66,76,87,100,114,129,
%T A242216 146,165,185,207,232,258,287,318,352,389,428,471,517,566,619,676,737,
%U A242216 802,872,947,1027,1112,1203,1300,1402,1512,1628,1751,1882,2020,2167,2322
%N A242216 Number of partitions of n into Heegner numbers, cf. A003173.
%C A242216 Heegner numbers = A003173(1..9) = {1,2,3,7,11,19,43,67,163}.
%H A242216 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeegnerNumber.html">Heegner Number</a>
%H A242216 Wikipedia, <a href="http://en.wikipedia.org/wiki/Heegner_number">Heegner number</a>
%e A242216 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;
%e A242216 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;
%e A242216 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.
%t A242216 heegnerNums = {1, 2, 3, 7, 11, 19, 43, 67, 163};
%t A242216 a[n_] := Length @ IntegerPartitions[n, All, heegnerNums];
%t A242216 Table[a[n], {n, 0, 55}] (* _Jean-François Alcover_, Jun 10 2019 *)
%o A242216 (Haskell)
%o A242216 a242216 = p [1,2,3,7,11,19,43,67,163] where
%o A242216    p _          0 = 1
%o A242216    p []         _ = 0
%o A242216    p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
%o A242216 (Magma) [#RestrictedPartitions(n,{1, 2, 3, 7, 11, 19, 43, 67, 163}):n in [1..60]]; // _Marius A. Burtea_, Jun 10 2019
%Y A242216 Cf. A242217.
%K A242216 nonn
%O A242216 0,3
%A A242216 _Reinhard Zumkeller_, May 07 2014