A199118 Number of partitions of n into terms of (1,3)-Ulam sequence, cf. A002859.

1, 1, 1, 2, 3, 4, 6, 7, 10, 13, 17, 21, 28, 34, 42, 52, 65, 78, 96, 113, 138, 165, 196, 231, 276, 322, 379, 442, 518, 600, 698, 803, 931, 1071, 1231, 1407, 1615, 1839, 2099, 2384, 2712, 3069, 3478, 3923, 4434, 4991, 5618, 6303, 7083, 7928, 8878, 9916, 11081

Offset

0,4

Links

Table of n, a(n) for n=0..52.

Eric Weisstein's World of Mathematics, Ulam Sequence

Wikipedia, Ulam number

Index entries for Ulam numbers

Example

The first terms of A002859 are 1, 3, 4, 5, 6, 8, 10, 12, 17, 21, ...
a(7) = #{6+1, 5+1+1, 4+3, 4+1+1+1, 3+3+1, 3+1+1+1+1, 7x1} = 7;
a(8) = #{8, 6+1+1, 5+3, 5+1+1+1, 4+4, 4+3+1, 4+1+1+1+1, 3+3+1+1, 3+1+1+1+1+1, 8x1} = 10.

Prog

(Haskell)
a199118 = p a002859_list where
   p _ 0 = 1
   p us'@(u:us) m | m < u     = 0
                  | otherwise = p us' (m - u) + p us m

Crossrefs

Cf. A000607; A199119, A199016, A199120, A199122.

Sequence in context: A355979 A119793 A181436 * A035941 A039854 A237752

Adjacent sequences: A199115 A199116 A199117 * A199119 A199120 A199121

Keyword

nonn

Author

Reinhard Zumkeller, Nov 03 2011

Status

approved