A090591 Expansion of g.f.: 1/(1 - 2*x + 8*x^2).

1, 2, -4, -24, -16, 160, 448, -384, -4352, -5632, 23552, 92160, -4096, -745472, -1458176, 3047424, 17760256, 11141120, -119799808, -328728576, 300941312, 3231711232, 4055891968, -17741905920, -67930947584

Offset: 0

Author

Simone Severini, Dec 04 2003

Keywords

• sign

Comments

(1,2) entry of powers of the orthogonal design shown below:

+1 +1 +1 +1 +1 +1 +1 +1

-1 +1 +1 -1 +1 -1 -1 +1

-1 -1 +1 +1 +1 +1 -1 -1

-1 +1 -1 +1 +1 -1 +1 -1

-1 -1 -1 -1 +1 +1 +1 +1

-1 +1 -1 +1 -1 +1 -1 +1

-1 +1 +1 -1 -1 +1 +1 -1

-1 -1 +1 +1 -1 -1 +1 +1

Pisano period lengths: 1, 1, 8, 1, 24, 8, 7, 1, 24, 24, 10, 8, 56, 7, 24, 1, 144, 24, 120, 24, ... - R. J. Mathar, Aug 10 2012

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-8).

Crossrefs

Cf. A087621, A090590.

Programs

GAP

a:=[1,2];; for n in [3..30] do a[n]:=2*a[n-1]-8*a[n-2]; od; a; # Muniru A Asiru, Oct 23 2018

Magma

[n le 2 select n else 2*Self(n-1) - 8*Self(n-2): n in [1..30]]; // G. C. Greubel, Oct 22 2018

Maple

seq(coeff(series(1/(1-2*x+8*x^2),x,n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Oct 23 2018

Mathematica

LinearRecurrence[{2,-8}, {1,2}, 30] (* G. C. Greubel, Oct 22 2018 *)
CoefficientList[Series[1/(1-2x+8x^2),{x,0,60}],x] (* Harvey P. Dale, Jan 17 2021 *)

PARI

x='x+O('x^30); Vec(1/(1 - 2*x + 8*x^2)) \\ G. C. Greubel, Oct 22 2018

Sage

[lucas_number1(n,2,8) for n in range(1, 21)] # Zerinvary Lajos, Apr 23 2009

Formula

Binomial transform of (1+x)/(1+7*x^2).

a(0)=1, a(1)=2, a(n) = 2*a(n-1) - 8*a(n-2) for n>1. - Philippe Deléham, Sep 19 2009

Extensions

Formulae from Paul Barry, Dec 05 2003

Corrected by T. D. Noe, Dec 11 2006