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A067902
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a(n) = 14*a(n-1) - a(n-2); a(0) = 2, a(1) = 14.
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3
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2, 14, 194, 2702, 37634, 524174, 7300802, 101687054, 1416317954, 19726764302, 274758382274, 3826890587534, 53301709843202, 742397047217294, 10340256951198914, 144021200269567502, 2005956546822746114, 27939370455248878094, 389145229826661547202, 5420093847118012782734
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Solves for x in x^2 - 3*y^2 = 4.
For n>0, a(n)+2 is the number of dimer tilings of a 4 X 2n Klein bottle (cf. A103999).
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)
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FORMULA
| G.f.: 2*(1-7*x)/(1-14*x+x^2). - N. J. A. Sloane (njas(AT)research.att.com), Nov 22 2006
a(n) = p^n + q^n, where p = 7 + 4*sqrt(3) and q = 7 - 4*sqrt(3). - Tanya Khovanova (tanyakh(AT)yahoo.com), Feb 06 2007
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MAPLE
| a := proc(n) option remember: if n=0 then RETURN(2) fi: if n=1 then RETURN(14) fi: 14*a(n-1)-a(n-2): end: for n from 0 to 30 do printf(`%d, `, a(n)) od:
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MATHEMATICA
| a[0] = 2; a[1] = 14; a[n_] := 14a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 16}] (from Robert G. Wilson v Jan 30 2004)
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PROG
| sage: [lucas_number2(n, 14, 1) for n in xrange(0, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 26 2008
(MAGMA) [Floor((2+Sqrt(3))^(2*n)+(1+Sqrt(3))^(-n)): n in [0..19]]; - Vincenzo Librandi, Mar 31 2011
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CROSSREFS
| Cf. A067900.
Row 2 * 2 of array A188644
Sequence in context: A191236 A074655 A158102 * A132611 A156327 A047796
Adjacent sequences: A067899 A067900 A067901 * A067903 A067904 A067905
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KEYWORD
| nonn
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AUTHOR
| Lekraj Beedassy (blekraj(AT)yahoo.com), May 13 2003
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