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%I #11 Sep 16 2018 13:00:49
%S 698901,5102520783381,37252493940331837461,
%T 271973082264557457061125141,1985621622943208359132836202790421,
%U 14496630316026749501691464257547633057301,105837027604506739193825102426073141683789429781,772695182809023513889440668692977953487035688873891861
%N Octagonal numbers (A000567) that are the sum of three consecutive octagonal numbers.
%H Colin Barker, <a href="/A258129/b258129.txt">Table of n, a(n) for n = 1..145</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7300803,-7300803,1).
%F G.f.: -21*x*(x^2 -844482*x +33281)/((x-1)*(x^2 -7300802*x +1)).
%e 698901 is in the sequence because Oct(483) = 698901 = 231296 + 232965 + 234640 = Oct(278) + Oct(279) + Oct(280).
%t CoefficientList[Series[-21*x*(x^2 -844482*x +33281)/((x-1)*(x^2 -7300802*x +1)), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 18 2017 *)
%t LinearRecurrence[{7300803,-7300803,1},{698901,5102520783381,37252493940331837461},20] (* _Harvey P. Dale_, Sep 16 2018 *)
%o (PARI) Vec(-21*x*(x^2 -844482*x +33281)/((x-1)*(x^2 -7300802*x +1)) + O('x^20))
%Y Cf. A000567, A258128, A258130, A258131, A258132.
%K nonn,easy
%O 1,1
%A _Colin Barker_, May 21 2015