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A129744
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a(n) = -(u^n-1)*(v^n-1) with u = 1+sqrt(2), v = 1-sqrt(2).
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0
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2, 4, 14, 32, 82, 196, 478, 1152, 2786, 6724, 16238, 39200, 94642, 228484, 551614, 1331712, 3215042, 7761796, 18738638, 45239072, 109216786, 263672644, 636562078, 1536796800, 3710155682, 8957108164, 21624372014, 52205852192
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431.
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FORMULA
| a(2n)=A002203(2n)-2. a(2n+1)=A002203(2n+1). - R. J. Mathar, corrected Dec 05 2007. O.g.f.: 2*x*(1+x^2)/((x^2+2*x-1)*(-1+x)*(1+x)).
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MAPLE
| u:=1+sqrt(2): v:=1-sqrt(2): a:=n->expand(-(u^n-1)*(v^n-1)): seq(a(n), n=1..33); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 13 2007
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MATHEMATICA
| Table[Simplify[ -((1 + Sqrt[2])^n - 1)*((1 - Sqrt[2])^n - 1)], {n, 1, 30}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), May 15 2007
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CROSSREFS
| Cf. A002003.
Sequence in context: A115626 A116021 A095977 * A148257 A148258 A148259
Adjacent sequences: A129741 A129742 A129743 * A129745 A129746 A129747
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 13 2007
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), May 13 2007
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