A199016 Number of partitions of n into terms of (1,2)-Ulam sequence, cf. A002858.

1, 1, 2, 3, 5, 6, 10, 12, 18, 22, 30, 37, 50, 60, 78, 94, 120, 143, 179, 213, 262, 309, 376, 440, 531, 618, 737, 855, 1012, 1167, 1372, 1575, 1840, 2104, 2442, 2783, 3214, 3649, 4193, 4746, 5430, 6126, 6980, 7853, 8914, 10002, 11311, 12660, 14274, 15934

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(6) = #{6, 4+2, 4+1+1, 3+3, 3+2+1, 3+1+1+1, 2+2+2, 2+2+1+1, 2+1+1+1+1, 1+1+1+1+1+1} = 10;
a(7) = #{6+1, 4+3, 4+2+1, 4+1+1+1, 3+3+1, 3+2+2, 3+2+1+1, 3+1+1+1+1, 2+2+2+1, 2+2+1+1+1, 2+1+1+1+1+1, 1+1+1+1+1+1+1} = 12.
		

Links

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

Crossrefs

Cf. A000607; A199017, A199118, A199120, A199122.

Programs

Haskell

199016 = p a002858_list where
   p _ 0 = 1
   p us'@(u:us) m | m < u     = 0
                  | otherwise = p us' (m - u) + p us m