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

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, 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, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 2, 3

Offset

0,4

Comments

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

0 <= a(n) <= 3;

for n > 316: a(n) = 0; 154 = smallest number m such that a(m) = 0;

number of terms greater than 0 = 303;

sum of all terms = 512.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..400

Eric Weisstein's World of Mathematics, Heegner Number

Wikipedia, Heegner number

Example

a(10) = #{7+3, 7+2+1} = 2;
a(11) = #{11, 7+3+1} = 2;
a(12) = #{11+1, 7+3+2} = 2;
a(13) = #{11+2, 7+3+2+1} = 2;
a(14) = #{11+3, 11+2+1} = 2;
a(15) = #{11+3+1} = 1;
a(16) = #{11+3+2} = 1;
a(17) = #{11+3+2+1} = 1;
a(18) = #{11+7} = 1;
a(19) = #{19, 11+7+1} = 2;
a(20) = #{19+1, 11+7+2} = 2;
a(316) = #{163+67+43+19+11+7+3+2+1} = 1.

Mathematica

heegnerNums = {1, 2, 3, 7, 11, 19, 43, 67, 163};
a[n_] := a[n] = Count[IntegerPartitions[n, All, heegnerNums], P_List /; Sort[P] == Union[P]];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 316}] (* Jean-François Alcover, Jun 10 2019 *)

Prog

(Haskell)
a242217 = p [1, 2, 3, 7, 11, 19, 43, 67, 163] where
   p _      0 = 1
   p []     _ = 0
   p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m

Crossrefs

Cf. A242216.

Sequence in context: A053258 A350738 A053632 * A306734 A124060 A329720

Adjacent sequences: A242214 A242215 A242216 * A242218 A242219 A242220

Keyword

nonn

Author

Reinhard Zumkeller, May 07 2014

Status

approved