A122603 - OEIS

%I #11 Mar 19 2017 13:56:39

%S 1,1,2,64,1509,27589,453949,7116398,108922001,1646720185,24736055959,

%T 370331348806,5534979578369,82658873060821,1233993261692386,

%U 18420012632366897,274961514388882353,4104700898601864514

%N 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 )

%C 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.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (43,-691,5146,-17903,25954,-11826,876,-1)

%t 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}]

%K nonn,less

%O 1,3

%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 20 2006