A301428 Number of compositions (ordered partitions) of n into prime parts such that no two adjacent parts are equal (Carlitz compositions).

1, 0, 1, 1, 0, 3, 0, 4, 3, 3, 10, 3, 16, 12, 18, 35, 24, 64, 57, 90, 137, 136, 259, 270, 416, 573, 679, 1088, 1264, 1869, 2491, 3199, 4691, 5834, 8341, 11053, 14685, 20595, 26636, 37199, 49449, 66572, 91377, 120733, 166151, 221912, 300038, 407775, 544843, 743318, 996752

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for sequences related to compositions

Formula

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

Example

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

Mathematica

nmax = 50; CoefficientList[Series[1/(1 - Sum[x^Prime[k]/(1 + x^Prime[k]), {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A003242, A023360, A218694, A219107.

Sequence in context: A322335 A245907 A104686 * A104514 A349915 A072480

Adjacent sequences: A301425 A301426 A301427 * A301429 A301430 A301431

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 21 2018

Status

approved