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

3,2

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).

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)

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 *)

Prog

(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
(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
(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
(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

Crossrefs

Cf. A000045, A027935.

Sequence in context: A137834 A178613 A124337 * A283629 A349742 A264626

Adjacent sequences: A027941 A027942 A027943 * A027945 A027946 A027947

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved