A193749 Number of partitions of n into distinct parts that are squares or triangular numbers (A005214).

1, 1, 0, 1, 2, 1, 1, 2, 1, 2, 4, 2, 1, 4, 4, 3, 5, 4, 3, 7, 7, 4, 6, 7, 6, 10, 10, 5, 10, 14, 10, 12, 14, 9, 14, 20, 13, 13, 20, 17, 18, 24, 17, 16, 27, 26, 22, 27, 25, 26, 35, 31, 26, 35, 37, 36, 42, 37, 35, 48, 47, 40, 49, 49, 48, 60, 58, 49, 61, 66, 61

Offset: 0

Author

Reinhard Zumkeller, Aug 03 2011

Keywords

• nonn

Examples

			a(10) = #{10, 9+1, 6+4, 6+3+1} = 4;
a(11) = #{10+1, 6+4+1} = 2;
a(12) = #{9+3} = 1;
a(13) = #{10+3, 9+4, 9+3+1, 6+4+3} = 4.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A000290, A000217, A033461, A024940, A193748, A000009.

Programs

Haskell

a193749 = p a005214_list where
   p _      0    = 1
   p (k:ks) m
     | m < k     = 0
     | otherwise = p ks (m - k) + p ks m