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Search: id:A156574
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| A156574 |
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a(n) = 34*a(n-1)-a(n-2)-4232 for n > 2; a(1)=1369, a(2)=42025. |
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4
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| 1369, 42025, 1423249, 48344209, 1642275625, 55789022809, 1895184495649, 64380483825025, 2187041265550969, 74295022544903689, 2523843725261170225, 85736391636334879729, 2912513471910124736329, 98939721653307906151225
(list; graph; listen)
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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+(627-238*sqrt(2))*(17+12*sqrt(2))^n+(627+238*sqrt(2))*(17-12*sqrt(2))^n)/8.
G.f.: x*(1369-5890*x+289*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*42025-1369-4232 = 1423249.
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PROGRAM
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(PARI) {m=14; v=concat([1369, 42025], 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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Third trisection of A156572.
Cf. A156164 (decimal expansion of 17+12*sqrt(2)), A156573, A156575.
Sequence in context: A015405 A020409 A167724 this_sequence A145697 A045107 A031752
Adjacent sequences: A156571 A156572 A156573 this_sequence A156575 A156576 A156577
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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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