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

0,4

Links

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

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A338887 A338886 A218950 * A364012 A322526 A364232

Adjacent sequences: A193745 A193746 A193747 * A193749 A193750 A193751

Keyword

nonn

Author

Reinhard Zumkeller, Aug 03 2011

Status

approved