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A027943 a(n) = T(2*n+1, n+3), T given by A027935. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 15 01:40 EDT 2019. Contains 328025 sequences. (Running on oeis4.)