A027944 a(n) = T(2n+1, n+4), T given by A027935.

1, 37, 376, 2267, 10220, 38403, 127921, 392688, 1140260, 3189022, 8699540, 23352118, 62048869, 163843187, 431026972, 1131463777, 2966502032, 7772382641, 20356549685, 53305176134, 139569431544, 365416760764, 956698453752, 2504701077772, 6557433205689, 17167634170241

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-43,105,-161,161,-105,43,-10,1).

Crossrefs

Cf. A000045, A027935.

Programs

GAP

List([3..30], n-> Fibonacci(2*n+9) - (8*n^6 +12*n^5 +110*n^4 +465*n^3 +1412*n^2 + 2943*n +3060)/90 ); # G. C. Greubel, Sep 28 2019

Magma

[Fibonacci(2*n+9) - (8*n^6 +12*n^5 +110*n^4 +465*n^3 +1412*n^2 + 2943*n +3060)/90: n in [3..30]]; // G. C. Greubel, Sep 28 2019

Maple

with(combinat); seq(fibonacci(2*n+9) -(8*n^6 +12*n^5 +110*n^4 +465*n^3 +1412*n^2 + 2943*n +3060)/90, n=3..30); # G. C. Greubel, Sep 28 2019

Mathematica

Table[Fibonacci[2*n+5] -(8*n^6 +12*n^5 +110*n^4 +465*n^3 +1412*n^2 + 2943*n +3060)/90, {n,3,30}] (* G. C. Greubel, Sep 28 2019 *)

PARI

vector(30, n, my(m=n+2); fibonacci(2*m+9) - (8*m^6 +12*m^5 +110*m^4 +465*m^3 +1412*m^2 + 2943*m +3060)/90) \\ G. C. Greubel, Sep 28 2019

Sage

[fibonacci(2*n+9) - (8*n^6 +12*n^5 +110*n^4 +465*n^3 +1412*n^2 + 2943*n +3060)/90 for n in (3..30)] # G. C. Greubel, Sep 28 2019

Formula

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

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

a(n) = Fibonacci(2*n+9) - (8*n^6 + 12*n^5 + 110*n^4 + 465*n^3 + 1412*n^2 + 2943*n + 3060)/90.

G.f.: x^3*(1 + 27*x + 49*x^2 - 7*x^3 - 6*x^4)/((1-x)^7*(1-3*x+x^2)). (End)

Extensions

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