A345007 a(0) = 1; a(3*n) = a(n) - a(n-1), a(3*n+1) = a(3*n+2) = -a(n).

1, -1, -1, -2, 1, 1, 0, 1, 1, -1, 2, 2, 3, -1, -1, 0, -1, -1, -1, 0, 0, 1, -1, -1, 0, -1, -1, -2, 1, 1, 3, -2, -2, 0, -2, -2, 1, -3, -3, -4, 1, 1, 0, 1, 1, 1, 0, 0, -1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, -1, -1, -2, 1, 1, 0, 1, 1, 1, 0, 0, -1, 1, 1, 0, 1, 1, -1, 2, 2, 3, -1, -1, 0, -1, -1, 2, -3, -3, -5, 2, 2

Offset

0,4

Links

Table of n, a(n) for n=0..95.

Formula

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

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

Mathematica

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, 95}]
nmax = 95; 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]
nmax = 95; 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]

Crossrefs

Cf. A054390, A177219, A309048, A345006.

Sequence in context: A290307 A206588 A302234 * A026920 A060763 A131576

Adjacent sequences: A345004 A345005 A345006 * A345008 A345009 A345010

Keyword

sign

Author

Ilya Gutkovskiy, Jun 05 2021

Status

approved