A199120 Number of partitions of n into terms of (1,4)-Ulam sequence, cf. A003666.

1, 1, 1, 1, 2, 3, 4, 5, 7, 8, 11, 13, 17, 20, 25, 30, 38, 44, 54, 63, 77, 90, 107, 124, 148, 171, 202, 231, 271, 310, 360, 412, 477, 542, 622, 705, 809, 915, 1042, 1175, 1335, 1501, 1699, 1905, 2148, 2403, 2702, 3018, 3383, 3768, 4212, 4682, 5223, 5794, 6445

Offset: 0

Author

Reinhard Zumkeller, Nov 03 2011

Keywords

• nonn

Examples

			The first terms of A003666 are 1, 4, 5, 6, 7, 8, 10, 16, 18, 19, ...
a(7) = #{7, 6+1, 5+1+1, 4+1+1+1, 7x1} = 5;
a(8) = #{8, 7+1, 6+1+1, 5+1+1+1, 4+4, 4+1+1+1+1, 8x1} = 7;
a(9) = #{8+1, 7+1+1, 6+1+1+1, 5+4, 5+1+1+1+1, 4+4+1, 4+5x1, 9x1} = 8.
		

Links

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

Crossrefs

Cf. A000607; A199016, A199118, A199121, A199122.

Programs

Haskell

a199120 = p a003666_list where
   p _ 0 = 1
   p us'@(u:us) m | m < u     = 0
                  | otherwise = p us' (m - u) + p us m