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A107328
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Even-indexed Lucas numbers + 1 (i.e. A000032(2n) + 1).
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0
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3, 4, 8, 19, 48, 124, 323, 844, 2208, 5779, 15128, 39604, 103683, 271444, 710648, 1860499, 4870848, 12752044, 33385283, 87403804, 228826128, 599074579, 1568397608, 4106118244, 10749957123, 28143753124
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Sum of n-th powers of roots of cubic polynomial x^3 - 4*x^2 + 4x - 1.
This real-root cubic polynomial is the characteristic polynomial generated by the Bombieri-like morphism: 1->{1,2,1},2->{1},3->{2,3}.
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FORMULA
| G.f.: (1-2*x)*(3-2*x)/((1-x)*(1+3*x-x^2)).
a(n)=A065034(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 24 2008]
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MATHEMATICA
| poly=Function[x, x^3-4*x^2+4x-1]; Table[RootSum[poly, Function[x, x^n]], {n, 0, 25}]
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PROG
| sage: [lucas_number2(n, 3, 1)+1 for n in xrange(0, 29)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 06 2008
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CROSSREFS
| Sequence in context: A183494 A107429 A061273 * A129285 A051440 A101932
Adjacent sequences: A107325 A107326 A107327 * A107329 A107330 A107331
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KEYWORD
| uned,nonn
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), May 22 2005
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EXTENSIONS
| Corrected and edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 11 2006
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