A199119 Number of partitions of n into distinct terms of (1,3)-Ulam sequence, cf. A002859.

1, 1, 0, 1, 2, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6, 7, 7, 8, 10, 9, 9, 12, 13, 13, 13, 14, 17, 18, 18, 19, 21, 23, 25, 26, 27, 30, 33, 33, 36, 40, 42, 43, 45, 51, 55, 55, 57, 62, 67, 71, 72, 76, 82, 87, 91, 95, 100, 107, 112, 116, 124, 132, 137, 143, 151, 159, 170

Offset: 0

Author

Reinhard Zumkeller, Nov 03 2011

Keywords

• nonn

Examples

			The first terms of A002859 are 1, 3, 4, 5, 6, 8, 10, 12, 17, 21, ...
a(10) = #{10, 6+4, 6+3+1, 5+4+1} = 4;
a(11) = #{10+1, 8+3, 6+5, 6+4+1} = 4;
a(12) = #{12, 8+4, 8+3+1, 6+5+1, 5+4+3} = 5.
		

Links

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

Crossrefs

A000586; A199118, A199017, A199121, A199123.

Programs

Haskell

a199119 = p a002859_list where
   p _  0 = 1
   p (u:us) m | m < u = 0
              | otherwise = p us (m - u) + p us m