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Octagonal numbers (A000567) that are the sum of ten consecutive octagonal numbers.
5

%I #13 Jul 25 2019 15:25:54

%S 1045,1325345,1910970885,2755618515265,3973599987865685,

%T 5729928426883626945,8262552817966202013445,

%U 11914595433578836419585185,17180838352667864150839647765,24774756989951626526674352316385,35725182398671892783600265200403845

%N Octagonal numbers (A000567) that are the sum of ten consecutive octagonal numbers.

%H Colin Barker, <a href="/A258130/b258130.txt">Table of n, a(n) for n = 1..316</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1443,-1443,1).

%F G.f.: -95*x*(63*x^2 - 1922*x + 11)/((x - 1)*(x^2 - 1442*x + 1)).

%e 1045 is in the sequence because Oct(19) = 1045 = 1+8+21+40+65+96+133+176+225+280 = Oct(1) + ... + Oct(10).

%t CoefficientList[Series[-95 x (63 x^2 - 1922 x + 11)/((x - 1) (x^2 - 1442 x + 1)), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 18 2017 *)

%t LinearRecurrence[{1443,-1443,1},{1045,1325345,1910970885},20] (* _Harvey P. Dale_, Jul 25 2019 *)

%o (PARI) Vec(-95*x*(63*x^2-1922*x+11)/((x-1)*(x^2-1442*x+1)) + O('x^20))

%Y Cf. A000567, A258128, A258129, A258131, A258132.

%K nonn,easy

%O 1,1

%A _Colin Barker_, May 21 2015