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Search: id:A155465
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| A155465 |
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a(n) = 7*a(n-1)-7*a(n-2)+a(n-3) for n > 2; a(0) = 7, a(1) = 88, a(2) = 555. |
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5
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| 7, 88, 555, 3276, 19135, 111568, 650307, 3790308, 22091575, 128759176, 750463515, 4374021948, 25493668207, 148587987328, 866034255795, 5047617547476, 29419671029095, 171470408627128, 999402780733707, 5824946275775148
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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) = 7, a(1) = 88.
a(n) = ((31+25*sqrt(2))*(3+2*sqrt(2))^n+(31-25*sqrt(2))*(3-2*sqrt(2))^n-34)/4.
G.f.: (7+39*x-12*x^2)/((1-x)*(1-6*x+x^2)).
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PROGRAM
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(PARI) {m=20; v=concat([7, 88, 555], 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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Second trisection of A118120. Cf. A001652.
Cf. A155464, A155466, A156035 (decimal expansion of 3+2*sqrt(2)).
Sequence in context: A034219 A034238 A132486 this_sequence A137143 A069430 A020564
Adjacent sequences: A155462 A155463 A155464 this_sequence A155466 A155467 A155468
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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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