A309048 - OEIS

%I #5 Jul 09 2019 13:30:14

%S 1,1,1,0,1,1,0,1,1,-1,0,0,1,1,1,0,1,1,-1,0,0,1,1,1,0,1,1,-2,-1,-1,1,0,

%T 0,0,0,0,1,1,1,0,1,1,0,1,1,-1,0,0,1,1,1,0,1,1,-2,-1,-1,1,0,0,0,0,0,1,

%U 1,1,0,1,1,0,1,1,-1,0,0,1,1,1,0,1,1,-3,-2,-2,1,-1,-1,0,-1,-1,2,1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1

%N Expansion of Product_{k>=0} (1 + x^(3^k) + x^(2*3^k) - x^(3^(k+1))).

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

%F a(0) = 1; a(3*n) = a(n) - a(n-1), a(3*n+1) = a(n), a(3*n+2) = a(n).

%t nmax = 109; CoefficientList[Series[Product[(1 + x^(3^k) + x^(2 3^k) - x^(3^(k + 1))), {k, 0, Floor[Log[3, nmax]] + 1}], {x, 0, nmax}], x]

%t nmax = 109; A[_] = 1; Do[A[x_] = (1 + x + x^2 - x^3) A[x^3] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

%t a[0] = 1; a[n_] := Switch[Mod[n, 3], 0, a[n/3] - a[(n - 3)/3], 1, a[(n - 1)/3], 2, a[(n - 2)/3]]; Table[a[n], {n, 0, 109}]

%Y Cf. A005590, A054390, A309047.

%K sign

%O 0,28

%A _Ilya Gutkovskiy_, Jul 09 2019