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

Author

Clark Kimberling

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000045, A027935.

Programs

GAP

List([1..40], n-> Fibonacci(2*n+5) -(2*n^2+5*n+5) ); # G. C. Greubel, Sep 28 2019

Magma

[Fibonacci(2*n+5)-2*n^2-5*n-5: n in [1..30]]; // Vincenzo Librandi, Apr 18 2011

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 *)

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

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

Extensions

More terms from Vincenzo Librandi, Oct 18 2013