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A345137
a(1) = a(2) = 1; a(n+2) = Sum_{d|n, d < n} a(d).
2
1, 1, 0, 1, 1, 2, 1, 2, 1, 3, 1, 3, 1, 5, 1, 3, 2, 5, 1, 5, 1, 7, 2, 3, 1, 10, 2, 3, 2, 9, 1, 9, 1, 8, 2, 4, 3, 14, 1, 3, 2, 14, 1, 11, 1, 11, 4, 4, 1, 16, 2, 7, 3, 14, 1, 12, 3, 14, 2, 4, 1, 27, 1, 3, 4, 17, 3, 13, 1, 13, 3, 14, 1, 23, 1, 5, 4, 18, 3, 16, 1, 20, 4, 4, 1, 32, 4, 3, 3, 24, 1, 25, 3, 16, 2
OFFSET
1,6
FORMULA
G.f. A(x) satisfies: A(x) = x + x^2 * (1 + A(x^2) + A(x^3) + A(x^4) + ...).
MATHEMATICA
a[1] = a[2] = 1; 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 (1 + Sum[A[x^k], {k, 2, nmax}]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 09 2021
STATUS
approved