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

0,6

Links

Table of n, a(n) for n=0..67.

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(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.

Prog

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

Crossrefs

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

Sequence in context: A099480 A025783 A025780 * A109697 A358903 A103373

Adjacent sequences: A199118 A199119 A199120 * A199122 A199123 A199124

Keyword

nonn

Author

Reinhard Zumkeller, Nov 03 2011

Status

approved