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 #23 Sep 08 2022 08:46:10
%S 1,50,4851,475300,46574501,4563825750,447208348951,43821854371400,
%T 4294094520048201,420777441110352250,41231895134294472251,
%U 4040304945719747928300,395908652785401002501101,38795007668023578497179550,3801514842813525291721094751
%N Indices of centered octagonal numbers (A016754) that are also pentagonal numbers (A000326).
%C Positive integers y in the solutions to 3*x^2 - 8*y^2 - x + 8*y - 2 = 0, the corresponding values of x being A046172.
%H Colin Barker, <a href="/A248205/b248205.txt">Table of n, a(n) for n = 1..503</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (99,-99,1).
%F a(n) = 99*a(n-1) - 99*a(n-2) + a(n-3).
%F G.f.: x*(49*x-1) / ((x-1)*(x^2 - 98*x + 1)).
%F a(n) = (1/2+1/48*(49+20*sqrt(6))^(-n)*(-12-5*sqrt(6)+(-12+5*sqrt(6))*(49+20*sqrt(6))^(2*n))). - _Colin Barker_, Mar 03 2016
%e 50 is in the sequence because the 50th centered octagonal number is 9801, which is also the 81st pentagonal number.
%t LinearRecurrence[{99, -99, 1}, {1, 50, 4851}, 20] (* _Vincenzo Librandi_, Jun 13 2015 *)
%o (PARI) Vec(x*(49*x-1)/((x-1)*(x^2-98*x+1)) + O(x^100))
%o (Magma) I:=[1,50,4851]; [n le 3 select I[n] else 99*Self(n-1)-99*Self(n-2)+Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jun 13 2015
%Y Cf. A000290, A000326, A046172, A036353.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Jan 11 2015