A107476 Expansion of -x*(-1+5*x+8*x^2-11*x^3+3*x^4)/(1-6*x-4*x^2+24*x^3-6*x^4-4*x^5+x^6) .

0, 1, 1, 2, 3, 5, 4, -13, -157, -1050, -6575, -39949, -241792, -1459663, -8809863, -53159766, -320770109, -1935508203, -11678751308, -70468796429, -425204036789

Offset

0,4

Comments

The sequence is generated by taking increasing powers of the matrix M = {{0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {-1, 4, 6, -24, 4, 6}}, multiplying the vector {0, 1, 1, 2, 3, 5} from the right and storing the product's upper element.

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (6,4,-24,6,4,-1).

Mathematica

m=4 M = {{0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {-1, m, (m + 2), -m*(m + 2), m, (m + 2)}} v[0] = {0, 1, 1, 2, 3, 5} v[n_] := M.v[n - 1] a = Table[Abs[v[n][[1]]], {n, 1, 50}]

Crossrefs

Sequence in context: A280690 A240000 A193770 * A094140 A119745 A095753

Adjacent sequences: A107473 A107474 A107475 * A107477 A107478 A107479

Keyword

sign

Author

Roger L. Bagula, May 27 2005

Extensions

Signed version reintroduced. - R. J. Mathar, Sep 11 2011

Status

approved