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%I #6 May 09 2019 15:00:09
%S 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,
%T 30,13,55,13,45,14,73,18,52,18,99,19,61,24,129,20,82,25,154,29,92,26,
%U 208,32,110,33,239,33,138,38,297,42,152,39,367,43,167,51,440,49,207,52,493,59,239
%N G.f. A(x) satisfies: A(x) = x + x^2 + x^3 + x^4 * (1 + A(x) + A(x^2) + A(x^3) + ...).
%C Shifts left 4 places under inverse Moebius transform.
%F G.f.: x + x^2 + x^3 + x^4 * (1 + Sum_{n>=1} a(n)*x^n/(1 - x^n)).
%F a(1) = ... = a(4) = 1; a(n+4) = Sum_{d|n} a(d).
%t 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]]
%t 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}]
%t 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}]
%Y Cf. A003238, A007439, A307993, A307995.
%K nonn
%O 1,6
%A _Ilya Gutkovskiy_, May 09 2019
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