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A088316
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a(n) = 13*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 13.
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17
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2, 13, 171, 2236, 29239, 382343, 4999698, 65378417, 854919119, 11179326964, 146186169651, 1911599532427, 24996980091202, 326872340718053, 4274337409425891, 55893258663254636, 730886700031736159, 9557420359075824703, 124977351368017457298, 1634262988143302769577
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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a(n) = ((13+sqrt(173))/2)^n + ((13-sqrt(173))/2)^n.
Lim_{n -> oo} a(n+1)/a(n) = (13 + sqrt(173))/2.
Lim_{n -> oo} a(n)/a(n+1) = 2/(13+sqrt(173)).
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MATHEMATICA
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LinearRecurrence[{13, 1}, {2, 13}, 31] (* Stefano Spezia, Sep 20 2022 *)
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PROG
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(Magma) I:=[2, 13]; [n le 2 select I[n] else 13*Self(n-1) +Self(n-2): n in [1..31]]; // G. C. Greubel, Dec 13 2022
(SageMath)
A088316=BinaryRecurrenceSequence(13, 1, 2, 13)
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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Nikolay V. Kosinov, Dmitry V. Polyakov (kosinov(AT)unitron.com.ua), Nov 06 2003
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STATUS
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approved
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