A301501 Number of compositions (ordered partitions) of n into prime power parts (A246655) such that no two adjacent parts are equal (Carlitz compositions).

1, 0, 1, 1, 1, 3, 2, 6, 5, 12, 14, 22, 35, 44, 79, 99, 165, 228, 346, 516, 742, 1140, 1624, 2479, 3592, 5370, 7933, 11684, 17421, 25557, 38098, 56053, 83207, 122958, 181848, 269426, 397900, 589749, 871302, 1290349, 1908208, 2823440, 4178248, 6179602, 9146534, 13527806, 20019958

Offset

0,6

Links

Table of n, a(n) for n=0..46.

Index entries for sequences related to compositions

Formula

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

Example

a(8) = 5 because we have [8], [5, 3], [3, 5], [3, 2, 3] and [2, 4, 2].

Mathematica

nmax = 46; CoefficientList[Series[1/(1 - Sum[Boole[PrimePowerQ[k]] x^k/(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A003242, A246655, A280195, A301428, A301500.

Sequence in context: A113782 A090868 A125675 * A072787 A338524 A371906

Adjacent sequences: A301498 A301499 A301500 * A301502 A301503 A301504

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 22 2018

Status

approved