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%I #9 Aug 16 2015 12:04:01
%S 560,4090071480,29860802042948800,218007803276760596488520,
%T 1591631806178550455562538466640,
%U 11620188673811755515268615201727379160,84836696710140620657577957851546090689242080,619375925014776443389412658082968133380998230391400
%N Positive octagonal numbers (A000567) that are other octagonal numbers divided by 3.
%H Colin Barker, <a href="/A259211/b259211.txt">Table of n, a(n) for n = 1..146</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7300803,-7300803,1).
%F a(n) = 7300803*a(n-1)-7300803*a(n-2)+a(n-3).
%F G.f.: -40*x*(x^2+40545*x+14) / ((x-1)*(x^2-7300802*x+1)).
%e 560 is in the sequence because 560 is the 14th octagonal number, and 3*560=1680 is the 24th octagonal number.
%t CoefficientList[Series[40 (x^2 + 40545 x + 14)/((1 - x) (x^2 - 7300802 x + 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 21 2015 *)
%o (PARI) Vec(-40*x*(x^2+40545*x+14)/((x-1)*(x^2-7300802*x+1)) + O(x^20))
%Y Cf. A000567, A076139, A121338, A259210.
%K nonn,easy
%O 1,1
%A _Colin Barker_, Jun 21 2015
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