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

Offset: 0

Author

Ilya Gutkovskiy, Jul 10 2019

Keywords

• nonn

Crossrefs

Cf. A000225 (positions of 1's), A000244, A023416, A048883, A080100, A080791, A309074.

Programs

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}]]

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).