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A242217 Number of partitions of n into distinct Heegner numbers, cf. A003173.

%I A242217 #9 Feb 16 2025 08:33:22
%S A242217 1,1,1,2,1,1,1,1,1,1,2,2,2,2,2,1,1,1,1,2,2,3,3,2,2,1,1,1,1,2,2,2,2,2,
%T A242217 1,1,1,1,1,1,2,1,1,2,1,1,2,1,1,1,1,1,1,2,2,2,2,2,1,1,1,1,2,2,3,3,2,3,
%U A242217 2,2,3,2,3,3,3,3,3,3,3,3,3,3,2,3,2,2,3
%N A242217 Number of partitions of n into distinct Heegner numbers, cf. A003173.
%C A242217 Heegner numbers = A003173(1..9) = {1,2,3,7,11,19,43,67,163};
%C A242217 0 <= a(n) <= 3;
%C A242217 for n > 316: a(n) = 0; 154 = smallest number m such that a(m) = 0;
%C A242217 number of terms greater than 0 = 303;
%C A242217 sum of all terms = 512.
%H A242217 Reinhard Zumkeller, <a href="/A242217/b242217.txt">Table of n, a(n) for n = 0..400</a>
%H A242217 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeegnerNumber.html">Heegner Number</a>
%H A242217 Wikipedia, <a href="http://en.wikipedia.org/wiki/Heegner_number">Heegner number</a>
%e A242217 a(10) = #{7+3, 7+2+1} = 2;
%e A242217 a(11) = #{11, 7+3+1} = 2;
%e A242217 a(12) = #{11+1, 7+3+2} = 2;
%e A242217 a(13) = #{11+2, 7+3+2+1} = 2;
%e A242217 a(14) = #{11+3, 11+2+1} = 2;
%e A242217 a(15) = #{11+3+1} = 1;
%e A242217 a(16) = #{11+3+2} = 1;
%e A242217 a(17) = #{11+3+2+1} = 1;
%e A242217 a(18) = #{11+7} = 1;
%e A242217 a(19) = #{19, 11+7+1} = 2;
%e A242217 a(20) = #{19+1, 11+7+2} = 2;
%e A242217 a(316) = #{163+67+43+19+11+7+3+2+1} = 1.
%t A242217 heegnerNums = {1,2,3,7,11,19,43,67,163};
%t A242217 a[n_] := a[n] = Count[IntegerPartitions[n, All, heegnerNums], P_List /; Sort[P] == Union[P]];
%t A242217 Table[Print[n," ", a[n]]; a[n], {n,0,316}] (* _Jean-François Alcover_, Jun 10 2019 *)
%o A242217 (Haskell)
%o A242217 a242217 = p [1,2,3,7,11,19,43,67,163] where
%o A242217    p _      0 = 1
%o A242217    p []     _ = 0
%o A242217    p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m
%Y A242217 Cf. A242216.
%K A242217 nonn
%O A242217 0,4
%A A242217 _Reinhard Zumkeller_, May 07 2014