A193748 Number of partitions of n into parts that are squares or triangular numbers (A005214).

1, 1, 1, 2, 3, 3, 5, 6, 7, 10, 13, 14, 19, 23, 26, 33, 41, 45, 56, 67, 76, 91, 108, 120, 143, 168, 188, 218, 255, 284, 328, 378, 422, 480, 551, 612, 695, 789, 876, 984, 1115, 1233, 1380, 1549, 1713, 1907, 2135, 2349, 2607, 2902, 3192, 3524, 3911, 4287, 4722

Offset: 0

Author

Reinhard Zumkeller, Aug 03 2011

Keywords

• nonn

Examples

			a(10) = #{10, 9+1, 6+4, 6+3+1, 6+1+1+1+1, 4+4+1+1, 4+3+3, 4+3+1+1+1, 4+6x1, 3+3+3+1, 3+3+1+1+1+1, 3+7x1, 10x1} = 13;
a(11) = #{10+1, 9+1+1, 6+4+1, 6+3+1+1, 6+1+1+1+1+1, 4+4+3, 4+4+1+1+1, 4+3+1+1+1+1, 4+7x1, 3+3+3+1+1, 3+3+5x1, 3+8x1, 11x1} = 14;
a(12) = #{10+1+1, 9+3, 9+1+1+1, 6+6, 6+4+1+1, 6+3+3, 6+3+1+1+1, 6+6x1, 4+4+4, 4+4+3+1, 4+4+1+1+1+1, 4+3+3+1+1, 4+3+5x1, 4+8x1, 3+3+3+3, 3+3+3+1+1+1, 3+3+6x1, 3+9x1, 12x1} = 19.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A000290, A000217, A001156, A007294, A193749, A000041.

Programs

Haskell

a193748 = p a005214_list where
   p _          0 = 1
   p ks'@(k:ks) m
     | m < k      = 0
     | otherwise  = p ks' (m - k) + p ks m