A345138 a(1) = 1, a(2) = 0; a(n+2) = Sum_{d|n, d < n} a(d).

1, 0, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 5, 2, 2, 1, 6, 2, 2, 2, 6, 1, 6, 1, 5, 2, 3, 3, 9, 1, 2, 2, 9, 1, 7, 1, 8, 4, 3, 1, 10, 2, 5, 3, 9, 1, 8, 3, 9, 2, 3, 1, 18, 1, 2, 4, 11, 3, 9, 1, 9, 3, 10, 1, 15, 1, 4, 4, 12, 3, 10, 1, 13, 4, 3, 1, 21, 4, 2, 3, 16, 1, 17, 3, 12, 2

Offset

1,10

Links

Table of n, a(n) for n=1..95.

Formula

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

Mathematica

a[1] = 1; a[2] = 0; a[n_] := a[n] = Sum[If[d < n - 2, a[d], 0], {d, Divisors[n - 2]}]; Table[a[n], {n, 1, 95}]
nmax = 95; A[_] = 0; Do[A[x_] = x + x^2 Sum[A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest

Crossrefs

Cf. A007439, A074206, A167865, A345137, A345141.

Sequence in context: A124768 A321014 A072527 * A343945 A081373 A029436

Adjacent sequences: A345135 A345136 A345137 * A345139 A345140 A345141

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 09 2021

Status

approved