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A090590
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(1,1) entry of powers of the orthogonal design shown below.
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2
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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; internal format)
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OFFSET
| 1,2
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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
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..202
Index to sequences with linear recurrences with constant coefficients, signature (2,-8).
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FORMULA
| G.f.: x*(1-8*x)/(1-2*x+8*x^2) - T. D. Noe, Dec 11 2006
Contribution by 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)
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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
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PROG
| Contribution by Bruno Berselli, Jun 24-25 2011: (Start)
(MAGMA) m:=27; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1-8*x)/(1-2*x+8*x^2)));
(Maxima) makelist(expand(((1+sqrt(-1)*sqrt(7))^n+(1-sqrt(-1)*sqrt(7))^n)/2), n, 1, 26);
(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 (End)
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CROSSREFS
| Cf. A087621, A090591.
Sequence in context: A060748 A176559 A075251 * A002566 A087998 A096823
Adjacent sequences: A090587 A090588 A090589 * A090591 A090592 A090593
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KEYWORD
| sign,easy
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AUTHOR
| Simone Severini (simoseve(AT)gmail.com), Dec 04 2003
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EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Dec 11 2006
More terms from Bruno Berselli, Jun 24 2011
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