A176758 a(n) = Sum_{k=0..floor((n-1)/2)} (3^k-1)*binomial(n, 2*k+1).

2, 8, 28, 88, 264, 768, 2192, 6176, 17248, 47872, 132288, 364416, 1001600, 2748416, 7532800, 20627968, 56452608, 154423296, 422276096, 1154447360, 3155544064, 8624177152, 23567831040, 64400793600, 175970803712, 480810303488

Offset: 3

Author

Roger L. Bagula, Apr 25 2010

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-2,-4).

Crossrefs

Cf. A002605, A094706.

Programs

Magma

I:=[2,8,28]; [n le 3 select I[n] else 4*Self(n-1) - 2*Self(n-2) +4*Self(n-3): n in [1..31]]; // G. C. Greubel, Sep 17 2021

Mathematica

(* First program *)
a[n_, q_]:= Sum[(q^((m-1)/2) - 1)*Binomial[n, m], {m,1,n,2}];
Table[a[n, 3], {n, 3, 30}]
(* Second program *)
A002605[n_]:= (-I*Sqrt[2])^(n-1)*ChebyshevU[n-1, I/Sqrt[2]];
Table[(Boole[n==0] - 2^n)/2 + A002605[n], {n, 3, 30}] (* G. C. Greubel, Sep 17 2021 *)

Sage

[(-i*sqrt(2))^(n-1)*chebyshev_U(n-1, i/sqrt(2)) - 2^(n-1) for n in (3..30)] # G. C. Greubel, Sep 17 2021

Formula

From R. J. Mathar, Jan 29 2012: (Start)

a(n) = A002605(n) - 2^(n-1) = 2*A094309(n).

G.f.: 2*x^3/( (1-2*x)*(1-2*x-2*x^2) ). (End)