OFFSET
0,3
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 10 2019
STATUS
approved