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, -2565652344946, -15480972873087, -93411142010973, -563636507934624, -3400944528117951, -20521069034764367

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..26.

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[v[n][[1]], {n, 0, 30}]

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 by R. J. Mathar, Sep 11 2011

More terms from Jason Yuen, Oct 05 2025

Status

approved