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Search: id:A156568
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| A156568 |
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a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1)=23, a(2)=115. |
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+0
4
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| 23, 115, 667, 3887, 22655, 132043, 769603, 4485575, 26143847, 152377507, 888121195, 5176349663, 30169976783, 175843511035, 1024891089427, 5973503025527, 34816127063735, 202923259356883, 1182723429077563
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OFFSET
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1,1
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COMMENT
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lim_{n -> infinity} a(n)/a(n-1) = 3+2*sqrt(2).
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FORMULA
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a(n) = 23*((2+sqrt(2))*(3-2*sqrt(2))^n +(2-sqrt(2))*(3+2*sqrt(2))^n)/4.
G.f.: 23*x*(1-x)/(1-6*x+x^2).
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PROGRAM
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(PARI) {m=19; v=concat([23, 115], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}
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CROSSREFS
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Second trisection of A156567. Equals 23*A001653.
Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156569, A156570.
Sequence in context: A142324 A070024 A057877 this_sequence A042026 A042028 A069756
Adjacent sequences: A156565 A156566 A156567 this_sequence A156569 A156570 A156571
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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), Feb 11 2009, Feb 16 2009
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EXTENSIONS
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G.f. corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 22 2009
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