A199122 Number of partitions of n into terms of (2,3)-Ulam sequence, cf. A001857.

1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 9, 11, 14, 16, 20, 23, 29, 33, 39, 47, 54, 64, 75, 86, 101, 117, 135, 155, 179, 204, 236, 268, 306, 349, 397, 450, 511, 577, 653, 736, 831, 934, 1050, 1179, 1322, 1478, 1657, 1848, 2065, 2302, 2562, 2852, 3172, 3518, 3909

Offset: 0

Author

Reinhard Zumkeller, Nov 03 2011

Keywords

• nonn

Examples

			The first terms of A001857 are 2, 3, 5, 7, 8, 9, 13, 14, 18, 19, ...
a(10) = #{8+2, 7+3, 5+5, 5+3+2, 3+3+2+2, 2+2+2+2+2} = 6;
a(11) = #{9+2, 8+3, 7+2+2, 5+3+3, 5+2+2+2, 3+3+3+2, 3+2+2+2+2} = 7;
a(12) = #{9+3, 8+2+2, 7+5, 7+3+2, 5+5+2, 5+3+2+2, 3+3+3+3, 3+3+2+2+2, 6x2} = 9.
		

Links

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

Crossrefs

Cf. A000607; A199123, A199016, A199118, A199120.

Programs

Haskell

a199122 = p a001857_list where
   p _ 0 = 1
   p us'@(u:us) m | m < u     = 0
                  | otherwise = p us' (m - u) + p us m

Mathematica

nmax = 60;
U = {2, 3};
Do[AppendTo[U, k = Last[U]; While[k++; Length[DeleteCases[Intersection[U, k - U], k/2, 1, 1]] != 2]; k], {nmax}];
a[n_] := IntegerPartitions[n, All, Select[U, # <= n &]] // Length;
Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Oct 12 2021 *)