A048906 Octagonal heptagonal numbers.
1, 297045, 69010153345, 16032576845184901, 3724720317758036481633, 865334473646149974640821781, 201036235582696134090746961388705, 46705140322177796790584365589105966085
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..100
- Eric Weisstein's World of Mathematics, Octagonal Heptagonal Number.
- Index entries for linear recurrences with constant coefficients, signature (232323,-232323,1).
Programs
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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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Mathematica
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 *)
Formula
From Harvey P. Dale, Dec 09 2011: (Start)
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)
From Ant King, Dec 30 2011: (Start)
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)
Comments