A027942 a(n) = T(2n+1, n+2), T given by A027935.

1, 11, 51, 176, 530, 1490, 4043, 10773, 28445, 74770, 196116, 513876, 1345861, 3524111, 9226935, 24157220, 63245318, 165579398, 433493615, 1134902265, 2971214081, 7778740966, 20365009896, 53316289896, 139583861065, 365435294675, 956722024443, 2504730780248

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (6,-13,13,-6,1).

Formula

a(n) = Fibonacci(2*n+5) - 2*n^2 - 5*n - 5.

G.f.: x*(1+5*x-2*x^2)/((1-x)^3*(1-3*x+x^2)). - Colin Barker, Sep 20 2012

Maple

with(combinat): seq(fibonacci(2*n+5) -(2*n^2+5*n+5), n=1..40); # G. C. Greubel, Sep 28 2019

Mathematica

CoefficientList[Series[(1+5x-2x^2)/((1-x)^3*(1-3x+x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 18 2013 *)
LinearRecurrence[{6, -13, 13, -6, 1}, {1, 11, 51, 176, 530}, 40] (* Harvey P. Dale, Aug 18 2017 *)

Prog

(Magma) [Fibonacci(2*n+5)-2*n^2-5*n-5: n in [1..30]]; // Vincenzo Librandi, Apr 18 2011
(PARI) vector(40, n, fibonacci(2*n+5) -(2*n^2+5*n+5) ) \\ G. C. Greubel, Sep 28 2019
(Sage) [fibonacci(2*n+5) -(2*n^2+5*n+5) for n in (1..40)] # G. C. Greubel, Sep 28 2019
(GAP) List([1..40], n-> Fibonacci(2*n+5) -(2*n^2+5*n+5) ); # G. C. Greubel, Sep 28 2019

Crossrefs

Cf. A000045, A027935.

Sequence in context: A185505 A051843 A107464 * A168214 A321421 A317021

Adjacent sequences: A027939 A027940 A027941 * A027943 A027944 A027945

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

More terms from Vincenzo Librandi, Oct 18 2013

Status

approved