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

0,6

Links

Table of n, a(n) for n=0..56.

Eric Weisstein's World of Mathematics, Ulam Sequence

Wikipedia, Ulam number

Index entries for Ulam numbers

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A014215 A067014 A096791 * A086740 A120161 A100665

Adjacent sequences: A199119 A199120 A199121 * A199123 A199124 A199125

Keyword

nonn

Author

Reinhard Zumkeller, Nov 03 2011

Status

approved