A345008 a(0) = 1; a(4*n) = a(n) - a(n-1), a(4*n+1) = a(4*n+2) = a(4*n+3) = a(n).

1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, -1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, -1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, -1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, -2, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, -1, 0, 0, 0, 1, 1, 1, 1, 0, 1

Offset: 0

Author

Ilya Gutkovskiy, Jun 05 2021

Keywords

• sign

Crossrefs

Cf. A005590, A277872, A309048, A345009.

Programs

Mathematica

a[0] = 1; a[n_] := Switch[Mod[n, 4], 0, a[n/4] - a[(n - 4)/4], 1, a[(n - 1)/4], 2, a[(n - 2)/4], 3, a[(n - 3)/4]]; Table[a[n], {n, 0, 105}]
nmax = 105; A[] = 1; Do[A[x] = (1 + x + x^2 + x^3 - x^4) A[x^4] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
nmax = 105; CoefficientList[Series[Product[(1 + x^(4^k) + x^(2 4^k) + x^(3 4^k) - x^(4^(k + 1))), {k, 0, Floor[Log[4, nmax]] + 1}], {x, 0, nmax}], x]

Formula

G.f. A(x) satisfies: A(x) = (1 + x + x^2 + x^3 - x^4) * A(x^4).

G.f.: Product_{k>=0} (1 + x^(4^k) + x^(2*4^k) + x^(3*4^k) - x^(4^(k+1))).