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

2,2

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).

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)

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}]

Prog

(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
(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
(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
(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

Crossrefs

Cf. A000045, A027935.

Sequence in context: A271635 A130438 A041934 * A224257 A244868 A223913

Adjacent sequences: A027940 A027941 A027942 * A027944 A027945 A027946

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved