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