A122010 - OEIS

%I #9 Mar 11 2022 13:20:10

%S 0,1,7,69,725,7679,81411,863197,9152557,97045551,1028984651,

%T 10910437661,115684573269,1226616283615,13005947679667,

%U 137903497048317,1462205981952029,15503931223058927,164389891941523323

%N G.f. x^2*(1-5*x)/(1-12*x+15*x^2-2*x^3).

%C Limit a(n+1)/a(n) = 10.6031 as n -> infinity.

%D "Linear Algebra, Examples and Applications" by Alain M. Robert, World Scientific, 2005, p. 58.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-15,2).

%F a(n)= 12*a(n-1) -15*a(n-2) +2*a(n-3).

%t M = {{1, 1, 1}, {1, 2, 4}, {1, 3, 9}} v[1] = {1, 0, 0} v[n_] := v[n] = M.v[n - 1] a1 = Table[v[n][[2]], {n, 1, 50}]

%t LinearRecurrence[{12,-15,2},{0,1,7},20] (* _Harvey P. Dale_, Mar 11 2022 *)

%Y Cf. A122009, A122011

%K nonn,easy

%O 1,3

%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 11 2006

%E Definition replaced with generating function by the Assoc. Eds. of the OEIS, Mar 27 2010