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Search: id:A156573
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| A156573 |
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a(n) = 34*a(n-1)-a(n-2)-4232 for n > 2; a(1)=529, a(2)=13225. |
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4
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| 529, 13225, 444889, 15108769, 513249025, 17435353849, 592288777609, 20120383080625, 683500735959409, 23218904639535049, 788759257008228025, 26794595833640213569, 910227499086759029089, 30920940373116166771225
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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) = 529*(2+(3-2*sqrt(2))*(17+12*sqrt(2))^n+(3+2*sqrt(2))*(17-12*sqrt(2))^n)/8.
G.f.: 529*x*(1-10*x+x^2)/((1-x)*(1-34*x+x^2)).
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EXAMPLE
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a(3) = 34*a(2)-a(1)-4232 = 34*13225-529-4232 = 444889.
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PROGRAM
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(PARI) {m=14; v=concat([529, 13225], 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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Second trisection of A156572. Equals 529*A008844.
Cf. A156164 (decimal expansion of 17+12*sqrt(2)), A156574, A156575.
Sequence in context: A067475 A052074 A112079 this_sequence A034987 A013773 A013907
Adjacent sequences: A156570 A156571 A156572 this_sequence A156574 A156575 A156576
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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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