A144476 Four interlaced copies of A117373.

1, 1, -1, 3, -2, -2, 2, 1, -3, -3, 3, -2, -1, -1, 1, -3, 2, 2, -2, -1, 3, 3, -3, 2, 1, 1, -1, 3, -2, -2, 2, 1, -3, -3, 3, -2, -1, -1, 1, -3, 2, 2, -2, -1, 3, 3, -3, 2, 1, 1, -1

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Oct 10 2008

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,0,0,0,-1).

Programs

Mathematica

Clear[M, v, n, a] M[0] = {{0, -1}, {1, 1}}; M[1] = {{1, 0}, {1, 1}}; M[2] = {{-1, 0}, {1, 1}}; M[3] = {{0, 1}, {1, 1}}; v[0] = {1, 1}; v[n_] := v[n] = M[Mod[n, 4]].v[n - 1]; a = Table[v[n][[1]], {n, 0, 50}]

Formula

a(n)=a(n-4)-a(n-8). a(4n+1)=a(4n+2)=A117373(n). a(4n+3)=A117373(n+3). a(4n+4)=A117373(n+5). [From R. J. Mathar, Dec 08 2008]

G.f.: -x*(2*x^7-3*x^6+3*x^5+3*x^4-3*x^3+x^2-x-1) / (x^8-x^4+1). - Colin Barker, Apr 11 2013