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

Author

Ilya Gutkovskiy, Mar 22 2018

Keywords

• nonn

Examples

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

Links

• Index entries for sequences related to compositions

Crossrefs

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

Programs

Mathematica

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

Formula

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