A199017 Number of partitions of n into distinct terms of (1,2)-Ulam sequence, cf. A002858.

1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 11, 12, 13, 14, 14, 16, 16, 17, 19, 20, 22, 23, 25, 26, 27, 29, 30, 31, 34, 35, 38, 40, 41, 45, 45, 48, 51, 52, 57, 60, 62, 66, 68, 71, 75, 78, 83, 86, 93, 97, 100, 107, 109, 115, 120, 124, 132, 138

Offset: 0

Author

Reinhard Zumkeller, Nov 03 2011

Keywords

• nonn

Examples

			The first terms of A002858 are 1, 2, 3, 4, 6, 8, 11, 13, 16, 18, ...
a(10) = #{8+2, 6+4, 6+3+1, 4+3+2+1} = 4;
a(11) = #{11, 8+3, 8+2+1, 6+4+1, 6+3+2} = 5;
a(12) = #{11+1, 8+4, 8+3+1, 6+4+2, 6+3+2+1} = 5.
		

Links

• Eric Weisstein's World of Mathematics, Ulam Sequence
• Wikipedia, Ulam number
• Index entries for Ulam numbers

Crossrefs

Cf. A000586; A199016, A199119, A199121, A199123.

Programs

Haskell

a199017 = p a002858_list where
   p _  0 = 1
   p (u:us) m | m < u = 0
              | otherwise = p us (m - u) + p us m