A199121 Number of partitions of n into distinct terms of (1,4)-Ulam sequence, cf. A003666.

1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6, 6, 7, 8, 7, 8, 10, 11, 11, 12, 14, 14, 15, 17, 18, 20, 21, 22, 24, 25, 27, 30, 31, 32, 35, 37, 39, 41, 44, 45, 48, 52, 53, 56, 60, 62, 66, 69, 72, 76, 81, 86, 89, 92, 96, 103, 109, 113, 117, 123, 127, 134

Offset: 0

Author

Reinhard Zumkeller, Nov 03 2011

Keywords

• nonn

Examples

			The first terms of A003666 are 1, 4, 5, 6, 7, 8, 10, 16, 18, 19, ...
a(12) = #{8+4, 7+5, 7+4+1, 6+5+1} = 4;
a(13) = #{8+5, 8+4+1, 7+6, 7+5+1} = 4;
a(14) = #{10+4, 8+6, 8+5+1, 7+6+1} = 4;
a(15) = #{10+5, 10+4+1, 8+7, 8+6+1, 6+5+4} = 5;
a(16) = #{16, 10+6, 10+5+1, 8+7+1, 7+5+4, 6+5+4+1} = 6.
		

Links

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

Crossrefs

Cf. A000586; A199120, A199017, A199119, A199123.

Programs

Haskell

a199121 = p a003666_list where
   p _  0 = 1
   p (u:us) m | m < u =
              | otherwise = p us (m - u) + p us m