A027955 a(n) = T(2n+1, n+3), T given by A027948.

1, 7, 92, 591, 2683, 9955, 32551, 98086, 280271, 773906, 2091266, 5576298, 14750858, 38839257, 101995694, 267462041, 700813797, 1835540197, 4806538617, 12585017712, 32949712457, 86265626164, 225849041524, 591283811748, 1548005222980, 4052735290427, 10610204784368

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-34,71,-90,71,-34,9,-1).

Crossrefs

Cf. A000045, A027948.

Programs

GAP

Concatenation([1], List([3..40], n-> Fibonacci(2*n+8) -(630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30) ); # G. C. Greubel, Sep 30 2019

Magma

[1] cat [Fibonacci(2*n+8) -(630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30: n in [3..40]]; // G. C. Greubel, Sep 30 2019

Maple

with(combinat); seq(`if`(n=2,1, fibonacci(2*n+8) -(630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30), n=2..40); # G. C. Greubel, Sep 30 2019

Mathematica

Table[If[n==2, 1, Fibonacci[2*n+8] - (630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30], {n,2,40}] (* G. C. Greubel, Sep 30 2019 *)

PARI

vector(40, n, my(m=n+1); if(m==2, 1, fibonacci(2*m+8) -(630 +607*m +295*m^2 +90*m^3 +20*m^4 +8*m^5)/30) ) \\ G. C. Greubel, Sep 30 2019

Sage

[1]+[fibonacci(2*n+8) -(630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30 for n in (3..40)] # G. C. Greubel, Sep 30 2019

Formula

G.f.: x^2*(1 -2*x +63*x^2 -70*x^3 +85*x^4 -71*x^5 +34*x^6 -9*x^7 +x^8)/( (1-x)^6*(1-3*x+x^2)). - Colin Barker, Nov 25 2014

From G. C. Greubel, Sep 30 2019: (Start)

a(n) = Sum_{j=0..n-2} binomial(2*n-j+1, j+6) for n >= 3.

a(n) = Fibonacci(2*n+8) - (630 +607*n +295*n^2 +90*n^3 +20*n^4 +8*n^5)/30 for n >= 3. (End)

Extensions

Name corrected and terms a(22) onward by G. C. Greubel, Sep 30 2019