Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Feb 19 2018 17:11:26
%S 5461,813281,7272157205,1083057360705,9684433559760981,
%T 1442322650052752161,12896895753596262561301,
%U 1920761265591267733640321,17174976631595008767000306005,2557904668044167195987033355105,22872156829955018609383449248248341
%N Octagonal numbers (A000567) that are the sum of two consecutive octagonal numbers.
%H Colin Barker, <a href="/A258128/b258128.txt">Table of n, a(n) for n = 1..326</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1331714,-1331714,-1,1).
%F G.f.: -x*(x^4+20*x^3-1146230*x^2+807820*x+5461) / ((x-1)*(x^2-1154*x+1)*(x^2+1154*x+1)).
%e 5461 is in the sequence because Oct(43) = 5461 = 2640 + 2821 = Oct(30) + Oct(31).
%t CoefficientList[Series[-x*(x^4 +20*x^3 -1146230*x^2 +807820*x +5461)/((x-1)*(x^2 -1154*x +1)*(x^2 +1154*x +1)), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 18 2017 *)
%t LinearRecurrence[{1,1331714,-1331714,-1,1},{5461,813281,7272157205,1083057360705,9684433559760981},20] (* _Harvey P. Dale_, Feb 19 2018 *)
%o (PARI) Vec(-x*(x^4 +20*x^3 -1146230*x^2 +807820*x +5461)/((x-1)*(x^2 -1154*x +1)*(x^2 +1154*x +1)) + O('x^20))
%Y Cf. A000567, A258129, A258130, A258131, A258132.
%K nonn,easy
%O 1,1
%A _Colin Barker_, May 21 2015