A027001 - OEIS

%I #14 Sep 08 2022 08:44:49

%S 1,26,174,743,2552,7784,22193,60882,163430,433495,1142496,3001056,

%T 7869649,20619098,54001422,141401879,370224248,969294632,2537687585,

%U 6643800690,17393752166,45537499111,119218794624,312118940928,817138091617,2139295405274

%N a(n) = T(2*n, n+2), T given by A026998.

%H Colin Barker, <a href="/A027001/b027001.txt">Table of n, a(n) for n = 2..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (7,-19,26,-19,7,-1).

%F a(n-2) = 3*F(2n+10)-2*F(2n+9)-F(2n+8)-4n^3-26n^2-68n-75, F(n) = A000045(n). - _Ralf Stephan_, Feb 07 2004

%F From _Colin Barker_, Feb 18 2016: (Start)

%F a(n) = (2^(-1-n)*(-11*2^(1+n)+(11-5*sqrt(5))*(3-sqrt(5))^n+(3+sqrt(5))^n*(11+5*sqrt(5)))-12*n-2*n^2-4*n^3).

%F G.f.: x^2*(1+x)*(1+18*x-7*x^2) / ((1-x)^4*(1-3*x+x^2)).

%F (End)

%t LinearRecurrence[{7, -19, 26, -19, 7, -1}, {1, 26, 174, 743, 2552, 7784}, 30] (* _Vincenzo Librandi_, Feb 19 2016 *)

%o (PARI) Vec(x^2*(1+x)*(1+18*x-7*x^2)/((1-x)^4*(1-3*x+x^2)) + O(x^40)) \\ _Colin Barker_, Feb 18 2016

%o (Magma) [3*Fibonacci(2*n+10)-2*Fibonacci(2*n+9)-Fibonacci(2*n+8)-4*n^3-26*n^2-68*n-75: n in [0..30]]; // _Vincenzo Librandi_, Feb 19 2016

%Y Bisection of A027964.

%K nonn,easy

%O 2,2

%A _Clark Kimberling_