A127978 a(n) = ((15*n + 34)/54)*2^(n-1) - (-1)^(n-1)*(6*n + 5)/27.

3, 5, 15, 31, 75, 163, 367, 799, 1747, 3771, 8119, 17367, 37019, 78579, 166271, 350735, 737891, 1548587, 3242823, 6776903, 14136363, 29437795, 61205775, 127071871, 263464435, 545570203, 1128423127, 2331411639, 4811954107

Offset: 2

Author

Artur Jasinski, Feb 09 2007

Keywords

• nonn
• easy

Comments

In the Bosma's paper there is an error (see table of the first few values at p. 37): for n=1 ((15*n+34)/54)*2^(n-1)-(-1)^(n-1)*(6*n+5)/27 is 1/2 and not 1.

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000
• W. Bosma, Signed bits and fast exponentiation, Journal de Théorie des Nombres de Bordeaux, Vol. 13, Fasc. 1 (2001), p. 38 (Proposition 7).
• Index entries for linear recurrences with constant coefficients, signature (2,3,-4,-4)

Crossrefs

Cf. A073371, A127976.

Programs

Magma

I:=[3, 5, 15, 31]; [n le 4 select I[n] else 2*Self(n-1) + 3*Self(n-2) -4*Self(n-3) -4*Self(n-4): n in [1..30]]; // G. C. Greubel, May 07 2018

Mathematica

Table[((15n+34)/54)2^(n-1) -((-1)^(n-1))(6n+5)/27, {n, 2, 50}]
LinearRecurrence[{2,3,-4,-4}, {3, 5, 15, 31}, 50] (* G. C. Greubel, May 07 2018 *)

PARI

x='x+O('x^30); Vec(x^2*(3-x-4*x^2-2*x^3)/((1+x)^2*(1-2*x)^2)) \\ G. C. Greubel, May 07 2018

Formula

G.f.: x^2*(3-x-4*x^2-2*x^3)/((1+x)^2*(1-2*x)^2). - Colin Barker, Apr 02 2012

Extensions

Offset changed from 1 to 2 (according to Bosma's Proposition 5) from Bruno Berselli, Apr 02 2012