A226748 Number of partitions of n into Platonic numbers, cf. A053012.

1, 1, 1, 1, 2, 2, 3, 3, 5, 5, 7, 7, 11, 11, 14, 14, 20, 20, 26, 27, 37, 37, 46, 47, 62, 63, 77, 80, 101, 103, 125, 130, 160, 164, 194, 203, 245, 253, 296, 311, 368, 381, 440, 463, 540, 562, 642, 677, 780, 814, 922, 973, 1107, 1157, 1302, 1375, 1552, 1626

Offset

0,5

Links

Table of n, a(n) for n=0..57.

Example

First Platonic numbers: 1, 4, 6, 8, 10, 12, 19, 20, ...
a(10) = #{10, 8+1+1, 6+4, 6+1+1+1+1, 4+4+1+1, 4+6x1, 10x1} = 7;
a(11) = #{10+1, 8+1+1+1, 6+4+1, 6+5x1, 4+4+1+1+1, 4+7x1, 11x1} = 7;
a(12) = #{12, 10+1+1, 8+4, 8+1+1+1+1, 6+6, 6+4+1+1, 6+6x1, 4+4+4, 4+4+1+1+1+1, 4+8x1, 12x1} = 11;
a(13) = #{12+1, 10+1+1+1, 8+4+1, 8+5x1, 6+6+1, 6+4+1+1+1, 6+7x1, 4+4+4+1, 4+4+5x1, 4+9x1, 13x1} = 11;
a(14) = #{12+1+1, 10+4, 10+1+1+1+1, 8+6, 8+4+1+1, 8+6x1, 6+6+1+1, 6+4+4, 6+4+1+1+1+1, 6+8x1, 4+4+4+1+1, 4+4+6x1, 4+10x1, 14x1} = 14;
a(15) = #{12+1+1+1, 10+4+1, 10+5x1, 8+6+1, 8+4+1+1+1, 8+7x1, 6+6+1+1+1, 6+4+4+1, 6+4+5x1, 6+9x1, 4+4+4+1+1+1, 4+4+7x1, 4+11x1, 15x1} = 14;
a(16) = #{12+4, 12+1+1+1+1, 10+6, 10+4+1+1, 10+6x1, 8+8, 8+6+1+1, 8+4+4, 8+4+1+1+1+1, 8+8x1, 6+6+4, 6+6+1+1+1+1, 6+4+4+1+1, 6+4+6x1, 6+10x1, 4+4+4+4, 4+4+4+1+1+1+1, 4+4+8x1, 4+12x1, 16x1} = 20.

Prog

(Haskell)
a226748 = p a053012_list where
   p _          0 = 1
   p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m

Crossrefs

Cf. A003108, A068980, A226749.

Sequence in context: A177716 A109763 A321523 * A119620 A240870 A265771

Adjacent sequences: A226745 A226746 A226747 * A226749 A226750 A226751

Keyword

nonn

Author

Reinhard Zumkeller, Jun 17 2013

Status

approved