A307994 G.f. A(x) satisfies: A(x) = x + x^2 + x^3 + x^4 * (1 + A(x) + A(x^2) + A(x^3) + ...).

1, 1, 1, 1, 1, 2, 2, 3, 2, 5, 3, 6, 4, 8, 4, 12, 5, 12, 7, 18, 6, 19, 8, 27, 10, 24, 9, 42, 12, 30, 13, 55, 13, 45, 14, 73, 18, 52, 18, 99, 19, 61, 24, 129, 20, 82, 25, 154, 29, 92, 26, 208, 32, 110, 33, 239, 33, 138, 38, 297, 42, 152, 39, 367, 43, 167, 51, 440, 49, 207, 52, 493, 59, 239

Offset

1,6

Comments

Shifts left 4 places under inverse Moebius transform.

Links

Table of n, a(n) for n=1..74.

Formula

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

a(1) = ... = a(4) = 1; a(n+4) = Sum_{d|n} a(d).

Mathematica

terms = 74; A[_] = 0; Do[A[x_] = x + x^2 + x^3 + x^4 (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 (1 + Sum[a[k] x^k/(1 - x^k), {k, 1, n - 1}]), {x, 0, n}]; Table[a[n], {n, 1, 74}]
a[n_] := a[n] = Sum[a[d], {d, Divisors[n - 4]}]; a[1] = a[2] = a[3] = a[4] = 1; Table[a[n], {n, 1, 74}]

Crossrefs

Cf. A003238, A007439, A307993, A307995.

Sequence in context: A078773 A151663 A162753 * A238480 A111089 A051664

Adjacent sequences: A307991 A307992 A307993 * A307995 A307996 A307997

Keyword

nonn

Author

Ilya Gutkovskiy, May 09 2019

Status

approved