A197081 Number of partitions of n into distinct positive quarter-squares (cf. A002620).

1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 3, 3, 2, 3, 4, 3, 4, 4, 4, 5, 6, 5, 4, 6, 6, 7, 7, 7, 7, 9, 10, 8, 9, 9, 11, 12, 12, 11, 11, 13, 15, 16, 13, 15, 16, 17, 20, 19, 17, 20, 23, 20, 22, 23, 23, 27, 29, 26, 25, 30, 31, 32, 34, 33, 32, 38, 41, 37, 39, 41, 42

Offset

0,7

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..555

Example

a(12) = #{12, 9+2+1, 6+4+2} = 3;
a(24) = #{20+4, 16+6+2, 12+9+2+1, 12+6+4+2} = 4.

Prog

(Haskell)
a197081 = p (drop 2 a002620_list) where
   p _      0             = 1
   p (k:ks) m | m < k     = 0
              | otherwise = p ks (m - k) + p ks m

Crossrefs

Cf. A197122, A002378, A000290, A000009.

Sequence in context: A352072 A365067 A332086 * A029395 A029282 A333123

Adjacent sequences: A197078 A197079 A197080 * A197082 A197083 A197084

Keyword

nonn

Author

Reinhard Zumkeller, Oct 10 2011

Status

approved