A027943 a(n) = T(2*n+1, n+3), T given by A027935.

1, 22, 155, 709, 2587, 8273, 24416, 68595, 187030, 500950, 1327986, 3499982, 9195035, 24115804, 63192397, 165512723, 433410661, 1134800215, 2971089810, 7778591025, 20364830496, 53316076892, 139583609940, 365435000524, 956721681957, 2504730383698, 6557469861231

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 (8,-26,45,-45,26,-8,1).

Crossrefs

Cf. A000045, A027935.

Programs

GAP

List([2..40], n-> Fibonacci(2*n+7) - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6 ); # G. C. Greubel, Sep 28 2019

Magma

[Fibonacci(2*n+7) - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6: n in [2..40]]; // G. C. Greubel, Sep 28 2019

Maple

with(combinat); seq(fibonacci(2*n+7) - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6, n=2..40); # G. C. Greubel, Sep 28 2019

Mathematica

Table[Fibonacci[2*n+7] - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6, {n,2,40}]

PARI

vector(30, n, my(m=n+1); fibonacci(2*m+7) - (4*m^4 +12*m^3 +35*m^2 +75*m +78)/6) \\ G. C. Greubel, Sep 28 2019

Sage

[fibonacci(2*n+7) - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6 for n in (2..40)] # G. C. Greubel, Sep 28 2019

Formula

G.f.: x^2*(1+14*x+5*x^2-4*x^3) / ((1-x)^5*(1-3*x+x^2)). - Colin Barker, Feb 20 2016

From G. C. Greubel, Sep 28 2019: (Start)

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

a(n) = Fibonacci(2*n+7) - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6. (End)

Extensions

Terms a(22) onward added by G. C. Greubel, Sep 28 2019