A307995 G.f. A(x) satisfies: A(x) = x + x^2 + x^3 + x^4 + x^5 * (1 + A(x) + A(x^2) + A(x^3) + ...).

1, 1, 1, 1, 1, 1, 2, 2, 3, 2, 4, 3, 5, 5, 5, 5, 8, 6, 9, 8, 10, 9, 13, 10, 14, 14, 15, 14, 20, 16, 21, 20, 24, 21, 28, 22, 30, 30, 31, 32, 39, 31, 41, 38, 48, 40, 52, 42, 54, 59, 55, 53, 67, 57, 78, 65, 75, 68, 85, 84, 91, 86, 90, 86, 124, 92, 109, 107, 116, 131, 133, 110, 139, 131, 171

Offset

1,7

Comments

Shifts left 5 places under inverse Moebius transform.

Links

Table of n, a(n) for n=1..75.

Formula

G.f.: x + x^2 + x^3 + x^4 + x^5 * (1 + Sum_{n>=1} a(n)*x^n/(1 - x^n)).

a(1) = ... = a(5) = 1; a(n+5) = Sum_{d|n} a(d).

Mathematica

terms = 75; A[_] = 0; Do[A[x_] = x + x^2 + x^3 + x^4 + x^5 (1 + Sum[A[x^k], {k, 1, terms}]) + O[x]^(terms + 1) // Normal, terms + 1]; Rest[CoefficientList[A[x], x]]
a[n_] := a[n] = SeriesCoefficient[x + x^2 + x^3 + x^4 + x^5 (1 + Sum[a[k] x^k/(1 - x^k), {k, 1, n - 1}]), {x, 0, n}]; Table[a[n], {n, 1, 75}]
a[n_] := a[n] = Sum[a[d], {d, Divisors[n - 5]}]; a[1] = a[2] = a[3] = a[4] = a[5] = 1; Table[a[n], {n, 1, 75}]

Crossrefs

Cf. A003238, A007439, A307993, A307994.

Sequence in context: A242112 A211316 A280226 * A061889 A240089 A218700

Adjacent sequences: A307992 A307993 A307994 * A307996 A307997 A307998

Keyword

nonn

Author

Ilya Gutkovskiy, May 09 2019

Status

approved