A309074 a(0) = 1; a(2*n) = 4*a(n), a(2*n+1) = a(n).

1, 1, 4, 1, 16, 4, 4, 1, 64, 16, 16, 4, 16, 4, 4, 1, 256, 64, 64, 16, 64, 16, 16, 4, 64, 16, 16, 4, 16, 4, 4, 1, 1024, 256, 256, 64, 256, 64, 64, 16, 256, 64, 64, 16, 64, 16, 16, 4, 256, 64, 64, 16, 64, 16, 16, 4, 64, 16, 16, 4, 16, 4, 4, 1, 4096, 1024, 1024, 256, 1024, 256, 256, 64, 1024, 256, 256, 64

Offset

0,3

Links

Table of n, a(n) for n=0..75.

Formula

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

a(0) = 1; for n > 0, a(n) = 4^(number of 0's in binary representation of n).

Mathematica

a[0] = 1; a[n_] := If[EvenQ[n], 4 a[n/2], a[(n - 1)/2]]; Table[a[n], {n, 0, 75}]
nmax = 75; A[_] = 1; Do[A[x_] = (4 + x) A[x^2] - 3 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Join[{1}, Table[4^Count[IntegerDigits[n, 2], 0], {n, 1, 75}]]

Crossrefs

Cf. A000225 (positions of 1's), A000302, A023416, A080100, A080791, A102376, A309057.

Sequence in context: A117292 A062780 A262616 * A175844 A351434 A167343

Adjacent sequences: A309071 A309072 A309073 * A309075 A309076 A309077

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 10 2019

Status

approved