A027940 a(n) = T(2*n, n+4), T given by A027935.

1, 46, 551, 3785, 18955, 77533, 276408, 895103, 2708322, 7811510, 21791338, 59419294, 159571139, 424302452, 1121168305, 2951121095, 7749900701, 20324325571, 53259796514, 139506540045, 365330860180, 956582678652, 2504546934692, 6557230277964, 17167369784405

Offset: 4

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 4..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-53,148,-266,322,-266,148,-53,11,-1).

Crossrefs

Cf. A000045, A027935.

Programs

GAP

List([4..40], n-> Fibonacci(2*n+9) - (21420 +20571*n +9961*n^2 +3304*n^3 +490*n^4 +364*n^5 -56*n^6 +16*n^7)/630 ); # G. C. Greubel, Sep 28 2019

Magma

[Fibonacci(2*n+9) - (21420 +20571*n +9961*n^2 +3304*n^3 +490*n^4 +364*n^5 -56*n^6 +16*n^7)/630: n in [4..40]]; // G. C. Greubel, Sep 28 2019

Maple

with(combinat); seq(fibonacci(2*n+9) - (21420 +20571*n +9961*n^2 +3304*n^3 +490*n^4 +364*n^5 -56*n^6 +16*n^7)/630, n=4..40); # G. C. Greubel, Sep 28 2019

Mathematica

Table[Fibonacci[2*n+9] - (21420 +20571*n +9961*n^2 +3304*n^3 +490*n^4 +364*n^5 -56*n^6 +16*n^7)/630, {n,4,40}] (* G. C. Greubel, Sep 28 2019 *)

PARI

vector(40, n, my(m=n+3); fibonacci(2*m+9) - (21420 +20571*m +9961*m^2 +3304*m^3 +490*m^4 +364*m^5 -56*m^6 +16*m^7)/630) \\ G. C. Greubel, Sep 28 2019

Sage

[fibonacci(2*n+9) - (21420 +20571*n +9961*n^2 +3304*n^3 +490*n^4 +364*n^5 -56*n^6 +16*n^7)/630 for n in (4..40)] # G. C. Greubel, Sep 28 2019

Formula

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

a(n) = Fibonacci(2*n+9) - (21420 + 20571*n + 9961*n^2 + 3304*n^3 + 490*n^4 + 364*n^5 - 56*n^6 + 16*n^7)/630.

G.f.: x^4*(1 + 35*x + 98*x^2 + 14*x^3 - 19*x^4 - x^5)/((1-x)^8*(1 - 3*x + x^2)). (End)

Extensions

Terms a(23) onward added by G. C. Greubel, Sep 28 2019