A308263 Number of ordered factorizations of n into Lucas numbers (beginning at 2) > 1.
1, 1, 1, 2, 0, 2, 1, 3, 1, 0, 1, 5, 0, 2, 0, 5, 0, 4, 0, 0, 2, 2, 0, 10, 0, 0, 1, 5, 1, 0, 0, 8, 2, 0, 0, 11, 0, 0, 0, 0, 0, 6, 0, 5, 0, 0, 1, 20, 1, 0, 0, 0, 0, 6, 0, 10, 0, 2, 0, 0, 0, 0, 3, 13, 0, 6, 0, 0, 0, 0, 0, 27, 0, 0, 0, 1, 2, 0, 0, 0, 1, 0, 0, 18, 0, 0, 2, 10
Offset: 1
Keywords
Crossrefs
Programs
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Mathematica
terms = 88; A[] = 0; Do[A[x] = x + A[x^2] + Sum[A[x^LucasL[k]], {k, 2, 25}] + O[x]^(terms + 1) // Normal, terms + 1]; Rest[CoefficientList[A[x], x]] f[n_] := f[n] = SeriesCoefficient[x^2 + Sum[x^LucasL[k], {k, 2, 25}], {x, 0, n}]; a[n_] := If[n == 1, n, Sum[If[d < n, f[n/d] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 88}]
Formula
G.f. A(x) satisfies: A(x) = x + A(x^2) + Sum_{k>=2} A(x^Lucas(k)).