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A048906
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Octagonal heptagonal numbers.
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4
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1, 297045, 69010153345, 16032576845184901, 3724720317758036481633, 865334473646149974640821781, 201036235582696134090746961388705, 46705140322177796790584365589105966085
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OFFSET
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1,2
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COMMENTS
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As n increases, this sequence is approximately geometric with common ratio r = lim(n->Infinity,a(n)/a(n-1)) = (sqrt(5)+sqrt(6))^8 = 116161+21208*sqrt(30). - Ant King, Dec 30 2011
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LINKS
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FORMULA
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G.f.: x*(-133*x^2-64722*x-1)/(x^3-232323*x^2+232323*x-1).
a(1)=1, a(2)=297045, a(3)=69010153345, a(n) = 232323*a(n-1)-232323*a(n-2)+a(n-3). (End)
a(n) = 232322*a(n-1)-a(n-2)+64856.
a(n) = 1/480*((17+2*sqrt(30))*(sqrt(5)+sqrt(6))^(8n-6)+(17-2*sqrt(30))*(sqrt(5)-sqrt(6))^(8n-6)-134).
a(n) = floor(1/480*(17+2*sqrt(30))*(sqrt(5)+sqrt(6))^(8n-6)). (End)
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MATHEMATICA
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CoefficientList[Series[(-133*x^2-64722*x-1)/(x^3-232323*x^2+ 232323*x- 1), {x, 0, 20}], x] (* or *) LinearRecurrence[{232323, -232323, 1}, {1, 297045, 69010153345}, 21] (* Harvey P. Dale, Dec 09 2011 *)
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PROG
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(Magma) I:=[1, 297045, 69010153345]; [n le 3 select I[n] else 232323*Self(n-1)-232323*Self(n-2)+Self(n-3): n in [1..15]]; // Vincenzo Librandi, Dec 28 2011
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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