A309057 - OEIS

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A309057

a(0) = 1; a(2*n) = 3*a(n), a(2*n+1) = a(n).

1, 1, 3, 1, 9, 3, 3, 1, 27, 9, 9, 3, 9, 3, 3, 1, 81, 27, 27, 9, 27, 9, 9, 3, 27, 9, 9, 3, 9, 3, 3, 1, 243, 81, 81, 27, 81, 27, 27, 9, 81, 27, 27, 9, 27, 9, 9, 3, 81, 27, 27, 9, 27, 9, 9, 3, 27, 9, 9, 3, 9, 3, 3, 1, 729, 243, 243, 81, 243, 81, 81, 27, 243, 81, 81, 27, 81, 27, 27, 9, 243

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..80.

FORMULA

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

a(0) = 1; for n > 0, a(n) = 3^(number of 0's in binary representation of n).

MATHEMATICA

a[0] = 1; a[n_] := If[EvenQ[n], 3 a[n/2], a[(n - 1)/2]]; Table[a[n], {n, 0, 80}]

nmax = 80; A[_] = 1; Do[A[x_] = (3 + x) A[x^2] - 2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Join[{1}, Table[3^Count[IntegerDigits[n, 2], 0], {n, 1, 80}]]