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

0,5

Links

Table of n, a(n) for n=0..54.

Eric Weisstein's World of Mathematics, Ulam Sequence

Wikipedia, Ulam number

Index entries for Ulam numbers

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A080655 A367358 A354816 * A118083 A241093 A116470

Adjacent sequences: A199117 A199118 A199119 * A199121 A199122 A199123

Keyword

nonn

Author

Reinhard Zumkeller, Nov 03 2011

Status

approved