A199017 Number of partitions of n into distinct terms of (1,2)-Ulam sequence, cf. A002858.

1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 11, 12, 13, 14, 14, 16, 16, 17, 19, 20, 22, 23, 25, 26, 27, 29, 30, 31, 34, 35, 38, 40, 41, 45, 45, 48, 51, 52, 57, 60, 62, 66, 68, 71, 75, 78, 83, 86, 93, 97, 100, 107, 109, 115, 120, 124, 132, 138

Offset

0,4

Links

Table of n, a(n) for n=0..66.

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(10) = #{8+2, 6+4, 6+3+1, 4+3+2+1} = 4;
a(11) = #{11, 8+3, 8+2+1, 6+4+1, 6+3+2} = 5;
a(12) = #{11+1, 8+4, 8+3+1, 6+4+2, 6+3+2+1} = 5.

Prog

(Haskell)
a199017 = p a002858_list where
   p _  0 = 1
   p (u:us) m | m < u = 0
              | otherwise = p us (m - u) + p us m

Crossrefs

Cf. A000586; A199016, A199119, A199121, A199123.

Sequence in context: A334415 A307152 A008671 * A189709 A025771 A154403

Adjacent sequences: A199014 A199015 A199016 * A199018 A199019 A199020

Keyword

nonn

Author

Reinhard Zumkeller, Nov 03 2011

Status

approved