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A309790
G.f. A(x) satisfies: A(x) = 2*x*(1 - x)*A(x^2) + x/(1 - x).
1
0, 1, 1, 3, -1, 3, -1, 7, -5, -1, 3, 7, -5, -1, 3, 15, -13, -9, 11, -1, 3, 7, -5, 15, -13, -9, 11, -1, 3, 7, -5, 31, -29, -25, 27, -17, 19, 23, -21, -1, 3, 7, -5, 15, -13, -9, 11, 31, -29, -25, 27, -17, 19, 23, -21, -1, 3, 7, -5, 15, -13, -9, 11, 63, -61, -57, 59
OFFSET
0,4
FORMULA
a(0) = 0; a(2*n+2) = -2*a(n) + 1, a(2*n+1) = 2*a(n) + 1.
MAPLE
a:= proc(n) option remember; `if`(n=0, 0, 2*
`if`(irem(n, 2, 'r')=0, -a(r-1), a(r))+1)
end:
seq(a(n), n=0..2^7-2); # Alois P. Heinz, Aug 29 2019
MATHEMATICA
nmax = 66; A[_] = 0; Do[A[x_] = 2 x (1 - x) A[x^2] + x/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 0; a[n_] := If[EvenQ[n], -2 a[(n - 2)/2] + 1, 2 a[(n - 1)/2] + 1]; Table[a[n], {n, 0, 66}]
CROSSREFS
Cf. A000225 (fixed points), A006257.
Compare also to the scatter plots of A117966, A317825.
Sequence in context: A318506 A322382 A122410 * A349619 A082495 A329385
KEYWORD
sign,look,hear
AUTHOR
Ilya Gutkovskiy, Aug 28 2019
STATUS
approved