A298732 Number of compositions (ordered partitions) of n into parts > 1 such that no two adjacent parts are equal (Carlitz compositions).

1, 0, 1, 1, 1, 3, 3, 6, 7, 14, 18, 30, 45, 66, 107, 157, 245, 369, 569, 862, 1325, 2020, 3078, 4717, 7183, 10991, 16769, 25626, 39117, 59763, 91264, 139362, 212893, 325060, 496525, 758258, 1158079, 1768634, 2701162, 4125320, 6300303, 9622247, 14695253, 22443451, 34276405, 52348435

Offset: 0

Author

Ilya Gutkovskiy, Jan 25 2018

Keywords

• nonn

Examples

			a(7) = 6 because we have [7], [5, 2], [4, 3], [3, 4], [2, 5] and [2, 3, 2].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for sequences related to compositions

Crossrefs

Cf. A000045, A002865, A003242, A011782, A025147, A032020, A114900, A155822, A212804, A218694.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1,
      add(`if`(j=i, 0, b(n-j, `if`(j<=n-j, j, 0))), j=2..n))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..50);  # Alois P. Heinz, Jan 25 2018

Mathematica

nmax = 45; CoefficientList[Series[1/(1 - Sum[x^k/(1 + x^k), {k, 2, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=2} x^k/(1 + x^k)).