A199123 Number of partitions of n into distinct terms of (2,3)-Ulam sequence, cf. A001857.

1, 0, 1, 1, 0, 2, 0, 2, 2, 2, 3, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 8, 8, 9, 11, 10, 12, 14, 12, 17, 16, 17, 22, 19, 24, 25, 25, 30, 30, 33, 37, 37, 42, 45, 46, 52, 54, 57, 64, 66, 69, 79, 76, 87, 93, 91, 109, 105, 115, 126, 123, 140, 144, 151, 166, 169, 180, 193

Offset

0,6

Links

Table of n, a(n) for n=0..67.

Eric Weisstein's World of Mathematics, Ulam Sequence

Wikipedia, Ulam number

Index entries for Ulam numbers

Example

The first terms of A001857 are 2, 3, 5, 7, 8, 9, 13, 14, 18, 19, 24, ...
a(20) = #{18+2, 13+7, 13+5+2, 9+8+3, 8+7+5, 8+7+3+2} = 6;
a(21) = #{19+2, 18+3, 14+7, 14+5+2, 13+8, 13+5+3, 9+7+5, 9+7+3+2} = 8.

Prog

(Haskell)
a199123 = p a001857_list where
   p _  0 = 1
   p (u:us) m | m < u = 0
              | otherwise = p us (m - u) + p us m

Crossrefs

Cf. A000586; A199122, A199017, A199119, A199121.

Sequence in context: A244478 A261153 A374078 * A394199 A385908 A325589

Adjacent sequences: A199120 A199121 A199122 * A199124 A199125 A199126

Keyword

nonn,changed

Author

Reinhard Zumkeller, Nov 03 2011

Status

approved