A307993 G.f. A(x) satisfies: A(x) = x + x^2 + x^3 * (1 + A(x) + A(x^2) + A(x^3) + ...).

1, 1, 1, 1, 2, 2, 3, 3, 5, 4, 6, 7, 8, 7, 13, 9, 12, 17, 15, 13, 27, 16, 22, 32, 24, 23, 48, 27, 33, 55, 40, 34, 79, 41, 49, 87, 55, 55, 122, 56, 72, 132, 81, 73, 174, 82, 98, 196, 106, 99, 253, 110, 131, 267, 144, 132, 342, 153, 175, 359, 188, 176, 459, 189, 218, 496, 238, 229, 602

Offset

1,5

Comments

Shifts left 3 places under inverse Moebius transform.

Links

Table of n, a(n) for n=1..69.

Formula

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

a(1) = a(2) = a(3) = 1; a(n+3) = Sum_{d|n} a(d).

Mathematica

terms = 69; A[_] = 0; Do[A[x_] = x + x^2 + x^3 (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 (1 + Sum[a[k] x^k/(1 - x^k), {k, 1, n - 1}]), {x, 0, n}]; Table[a[n], {n, 1, 69}]
a[n_] := a[n] = Sum[a[d], {d, Divisors[n - 3]}]; a[1] = a[2] = a[3] = 1; Table[a[n], {n, 1, 69}]

Crossrefs

Cf. A003238, A007439, A307994, A307995.

Sequence in context: A248519 A326670 A361178 * A114092 A082500 A194451

Adjacent sequences: A307990 A307991 A307992 * A307994 A307995 A307996

Keyword

nonn

Author

Ilya Gutkovskiy, May 09 2019

Status

approved