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A301501 Number of compositions (ordered partitions) of n into prime power parts (A246655) such that no two adjacent parts are equal (Carlitz compositions). 1
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 (list; graph; refs; listen; history; text; internal format)
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 A293549 A306443

Adjacent sequences:  A301498 A301499 A301500 * A301502 A301503 A301504

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 22 2018

STATUS

approved

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Last modified April 6 11:38 EDT 2020. Contains 333273 sequences. (Running on oeis4.)