|
| |
|
|
A002249
|
|
a(n)=a(n-1)-2*a(n-2).
|
|
9
| |
|
|
2, 1, -3, -5, 1, 11, 9, -13, -31, -5, 57, 67, -47, -181, -87, 275, 449, -101, -999, -797, 1201, 2795, 393, -5197, -5983, 4411, 16377, 7555, -25199, -40309, 10089, 90707, 70529, -110885, -251943, -30173, 473713, 534059, -413367, -1481485
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
COMMENTS
| 4*2^n = A002249(n)^2+7*A001607(n)^2. See A077020, A077021.
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=0..500
|
|
|
FORMULA
| G.f.: (2-x)/(1-x+2x^2). - Michael Somos, Oct 18, 2002
a(n) = trace(A^n) for the square matrix A=[1, -2;1, 0]. - Paul Barry (pbarry(AT)wit.ie), Sep 05 2003
a(n)=2^((n+2)/2)cos(-n*acot(sqrt(7)/7)) - Paul Barry (pbarry(AT)wit.ie), Sep 06 2003
|
|
|
MAPLE
| A002249 := proc(n) option remember; >if n = 1 then 1 elif n = 2 then -3 else A002249(n-1>)-2*A002249(n-2); fi; end;
|
|
|
PROG
| (PARI) a(n)=if(n<0, 0, polsym(2-x+x^2, n)[n+1])
(PARI) a(n)=if(n<0, 0, 2*real(((1+quadgen(-28))/2)^n))
(Other) sage: [lucas_number2(n, 1, 2) for n in xrange(0, 40)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2009]
|
|
|
CROSSREFS
| Cf. A014551.
Sequence in context: A058168 A058169 A178074 * A157127 A066748 A106583
Adjacent sequences: A002246 A002247 A002248 * A002250 A002251 A002252
|
|
|
KEYWORD
| sign,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Iwan Duursma (duursma(AT)research.att.com)
|
| |
|
|
