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A155464
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a(n) = 7*a(n-1)-7*a(n-2)+a(n-3) for n > 2; a(0) = 0, a(1) = 51, a(2) = 340.
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4
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0, 51, 340, 2023, 11832, 69003, 402220, 2344351, 13663920, 79639203, 464171332, 2705388823, 15768161640, 91903581051, 535653324700, 3122016367183, 18196444878432, 106056652903443, 618143472542260, 3602804182350151
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| lim_{n -> infinity} a(n+1)/a(n) = 3+2*sqrt(2).
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (7,-7,1).
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FORMULA
| a(n) = 6*a(n-1)-a(n-2)+34 for n > 1; a(0) = 0, a(1) = 51.
a(n) = ((1+sqrt(2))*(3+2*sqrt(2))^n+(1-sqrt(2))*(3-2*sqrt(2))^n-2)*17/4.
G.f.: 17*x*(3-x)/((1-x)*(1-6*x+x^2)).
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PROG
| (PARI) {m=20; v=concat([0, 51, 340], 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
| First trisection of A118120. Equals 17*A001652.
Cf. A155465, A155466, A156035 (decimal expansion of 3+2*sqrt(2)).
Sequence in context: A193250 A204717 A204956 * A165087 A152579 A083669
Adjacent sequences: A155461 A155462 A155463 * A155465 A155466 A155467
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KEYWORD
| nonn,easy
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AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 30 2009
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EXTENSIONS
| Comment and recursion formula added, cross-references edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 23 2009
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