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Search: id:A156575
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| A156575 |
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a(n) = 34*a(n-1)-a(n-2)-4232 for n > 2; a(1)=289, a(2)=4225. |
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+0
4
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| 289, 4225, 139129, 4721929, 160402225, 5448949489, 185103876169, 6288082836025, 213609712544449, 7256442143671009, 246505423172265625, 8373927945713356009, 284467044731081834449, 9663505592911069011025
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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) = 17+12*sqrt(2).
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FORMULA
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a(n) = (1058+(4947-3478*sqrt(2))*(17+12*sqrt(2))^n+(4947+3478*sqrt(2))*(17-12*sqrt(2))^n)/8.
G.f.: x*(289-5890*x+1369*x^2)/((1-x)*(1-34*x+x^2)).
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EXAMPLE
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a(4) = 34*a(3)-a(2)-4232 = 34*139129-4225-4232 = 4721929.
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PROGRAM
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(PARI) {m=14; v=concat([289, 4225], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-4232); v}
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CROSSREFS
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First trisection of A156572.
Cf. A156164 (decimal expansion of 17+12*sqrt(2)), A156573, A156574.
Sequence in context: A157990 A112077 A152934 this_sequence A156161 A114762 A125249
Adjacent sequences: A156572 A156573 A156574 this_sequence A156576 A156577 A156578
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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
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EXTENSIONS
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Revised by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 16 2009
G.f. corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 22 2009
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