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

1,4

Links

Table of n, a(n) for n=1..88.

Formula

G.f. A(x) satisfies: A(x) = x + A(x^2) + Sum_{k>=2} A(x^Lucas(k)).

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}]

Crossrefs

Cf. A000032, A102460, A200381 (positions of nonzero terms), A200995 (positions of zeros), A308062.

Sequence in context: A339242 A339222 A191247 * A028932 A076473 A163160

Adjacent sequences: A308260 A308261 A308262 * A308264 A308265 A308266

Keyword

nonn

Author

Ilya Gutkovskiy, May 17 2019

Status

approved