A090592 (1,1) entry of powers of the orthogonal design shown below.

1, -5, -17, 1, 121, 235, -377, -2399, -2159, 12475, 40063, -7199, -294839, -539285, 985303, 5745601, 4594081, -31031045, -94220657, 28776001, 717096601, 1232761195, -2554153817, -13737635999, -9596195279, 76971061435, 221115489823, -96566450399, -1740941329559

Offset

1,2

Comments

1 0 1 1 1 1 1 1

0 1 1 -1 1 -1 -1 1

-1 -1 1 0 1 1 -1 -1

-1 1 0 1 1 -1 1 -1

-1 -1 -1 -1 1 0 1 1

-1 1 -1 1 0 1 -1 1

-1 1 1 -1 -1 1 1 0

-1 -1 1 1 -1 -1 0 1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,-7).

Formula

a(1) = 1, a(2) = -5, a(n) = 2*a(n-1) - 7*a(n-2). - Philippe Deléham, Mar 05 2012

G.f.: x*(1-7*x)/(1-2*x+7*x^2). - Philippe Deléham, Mar 05 2012

G.f.: G(0)/(2*x) -1/x, where G(k)= 1 + 1/(1 - x*(6*k+1)/(x*(6*k+7) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 03 2013

Mathematica

Rest[CoefficientList[Series[x*(1-7*x)/(1-2*x+7*x^2), {x, 0, 30}], x]] (* G. C. Greubel, Oct 22 2018 *)

Prog

(PARI) x='x+O('x^30); Vec(x*(1-7*x)/(1-2*x+7*x^2)) \\ G. C. Greubel, Oct 22 2018
(Magma) I:=[1, -5]; [n le 2 select I[n] else 2*Self(n-1) - 7*Self(n-2): n in [1..30]]; // G. C. Greubel, Oct 22 2018
(GAP) a:=[1, -5];; for n in [3..30] do a[n]:=2*a[n-1]-7*a[n-2]; od; a; # Muniru A Asiru, Oct 23 2018

Crossrefs

Cf. A089181.

Sequence in context: A160739 A092679 A277534 * A340706 A093558 A170866

Adjacent sequences: A090589 A090590 A090591 * A090593 A090594 A090595

Keyword

sign,easy

Author

Simone Severini, Dec 08 2003

Extensions

Corrected and extended by Philippe Deléham, Mar 05 2012

Status

approved