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

0,2

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).

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

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 *)

Prog

(Sage) [lucas_number1(n, 2, 8) for n in range(1, 21)] # Zerinvary Lajos, Apr 23 2009
(PARI) x='x+O('x^30); Vec(1/(1 - 2*x + 8*x^2)) \\ G. C. Greubel, Oct 22 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
(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

Crossrefs

Cf. A087621, A090590.

Sequence in context: A269573 A147761 A214299 * A098656 A138611 A171459

Adjacent sequences: A090588 A090589 A090590 * A090592 A090593 A090594

Keyword

sign

Author

Simone Severini, Dec 04 2003

Extensions

Formulae from Paul Barry, Dec 05 2003

Corrected by T. D. Noe, Dec 11 2006

Status

approved