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Search: id:A155466
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| A155466 |
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a(n) = 7*a(n-1)-7*a(n-2)+a(n-3) for n > 2; a(0) = 28, a(1) = 207, a(2) = 1248. |
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5
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| 28, 207, 1248, 7315, 42676, 248775, 1450008, 8451307, 49257868, 287095935, 1673317776, 9752810755, 56843546788, 331308470007, 1931007273288, 11254735169755, 65597403745276, 382329687301935, 2228380720066368
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OFFSET
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0,1
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COMMENT
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lim_{n -> infinity} a(n+1)/a(n) = 3+2*sqrt(2).
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FORMULA
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a(n) = 6*a(n-1)-a(n-2)+34 for n > 1; a(0) = 28, a(1) = 207.
a(n) = ((73+53*sqrt(2))*(3+2*sqrt(2))^n+(73-53*sqrt(2))*(3-2*sqrt(2))^n-34)/4.
G.f.: (28+11*x-5*x^2)/((1-x)*(1-6*x+x^2)).
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PROGRAM
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(PARI) {m=19; v=concat([28, 207, 1248], vector(m-3)); for(n=4, m, v[n]=7*v[n-1]-7*v[n-2]+v[n-3]); v}
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CROSSREFS
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Third trisection of A118120. Cf. A001652.
Cf. A155464, A155465, A156035 (decimal expansion of 3+2*sqrt(2)).
Sequence in context: A135826 A042526 A159542 this_sequence A053135 A133071 A135180
Adjacent sequences: A155463 A155464 A155465 this_sequence A155467 A155468 A155469
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 30 2009
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EXTENSIONS
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Comment and recursion formula added, cross-references edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 23 2009
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