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

0,3

Links

Table of n, a(n) for n=0..49.

Eric Weisstein's World of Mathematics, Ulam Sequence

Wikipedia, Ulam number

Index entries for Ulam numbers

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A241443 A023025 A130898 * A088314 A304405 A347446

Adjacent sequences: A199013 A199014 A199015 * A199017 A199018 A199019

Keyword

nonn

Author

Reinhard Zumkeller, Nov 03 2011

Status

approved