login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A090590 (1,1) entry of powers of the orthogonal design shown below. 3
1, -6, -20, 8, 176, 288, -832, -3968, -1280, 29184, 68608, -96256, -741376, -712704, 4505600, 14712832, -6619136, -130940928, -208928768, 629669888, 2930769920, 824180736, -21797797888, -50189041664, 74004299776, 549520932864 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

+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

Also real part of (1 +- i*sqrt(7))^n. - Bruno Berselli, Jun 24-25 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..202

Index entries for linear recurrences with constant coefficients, signature (2,-8).

FORMULA

G.f.: x*(1-8*x)/(1-2*x+8*x^2). - T. D. Noe, Dec 11 2006

From Bruno Berselli, Jun 24-25 2011: (Start)

a(n) = (1/2)*((1+i*sqrt(7))^n + (1-i*sqrt(7))^n), where i=sqrt(-1).

a(n) = cos(n*arctan(sqrt(7)))*sqrt(8)^n.

a(n) = 2*a(n-1) - 8*a(n-2) (n > 2). (End)

MAPLE

a := proc(n) option remember: if(n=1)then return 1:elif(n=2)then return -6:fi: return 2*a(n-1)-8*a(n-2): end: seq(a(n), n=1..26); # Nathaniel Johnston, Jun 25 2011

MATHEMATICA

LinearRecurrence[{2, -8}, {1, -6}, 30] (* Harvey P. Dale, Mar 30 2019 *)

PROG

(Magma) m:=27; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1-8*x)/(1-2*x+8*x^2))); // Bruno Berselli, Jun 24-25 2011

(Maxima) makelist(expand(((1+sqrt(-1)*sqrt(7))^n+(1-sqrt(-1)*sqrt(7))^n)/2), n, 1, 26); /* Bruno Berselli, Jun 24-25 2011 */

(PARI) a=vector(26); a[1]=1; a[2]=-6; for(i=3, #a, a[i]=2*a[i-1]-8*a[i-2]); a \\ Bruno Berselli, Jun 24-25 2011

CROSSREFS

Cf. A087621, A090591.

Sequence in context: A282377 A281936 A075251 * A002566 A087998 A096823

Adjacent sequences: A090587 A090588 A090589 * A090591 A090592 A090593

KEYWORD

sign,easy

AUTHOR

Simone Severini, Dec 04 2003

EXTENSIONS

Corrected by T. D. Noe, Dec 11 2006

More terms from Bruno Berselli, Jun 24 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 09:11 EST 2022. Contains 358654 sequences. (Running on oeis4.)