A122603 Expansion of x*(1-42*x+650*x^2-4477*x^3+12896*x^4-11417*x^5+2675*x^6+110*x^7) / ( 1-43*x+691*x^2-5146*x^3+17903*x^4-25954*x^5+11826*x^6-876*x^7+x^8 )

1, 1, 2, 64, 1509, 27589, 453949, 7116398, 108922001, 1646720185, 24736055959, 370331348806, 5534979578369, 82658873060821, 1233993261692386, 18420012632366897, 274961514388882353, 4104700898601864514

Offset

1,3

Comments

Obtained as the top element of the vector resulting from multiplying the n-th power of the 8 X 8 matrix [[0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1], [-1, -4, 10, 10, -15, -6, 7, 1]] with the column vector which contains only 1's.

Links

Table of n, a(n) for n=1..18.

Index entries for linear recurrences with constant coefficients, signature (43,-691,5146,-17903,25954,-11826,876,-1)

Mathematica

M = {{0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}, {-1, -4, 10, 10, -15, -6, 7, 1}}; v[1] = Table[1, {n, 1, 8}]; v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, 100, 4}]

Crossrefs

Sequence in context: A223121 A134939 A217268 * A127691 A013822 A010047

Adjacent sequences: A122600 A122601 A122602 * A122604 A122605 A122606

Keyword

nonn,less

Author

Roger L. Bagula and Gary W. Adamson, Sep 20 2006

Status

approved