This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A253447 #17 Oct 07 2020 12:10:16 %S A253447 1,15,435,13021,390181,11692395,350381655,10499757241,314642335561, %T A253447 9428770309575,282548466951675,8467025238240661,253728208680268141, %U A253447 7603379235169803555,227847648846413838495,6827826086157245351281,204606934935870946699921 %N A253447 Indices of centered octagonal numbers (A016754) which are also centered heptagonal numbers (A069099). %C A253447 Also positive integers y in the solutions to 7*x^2 - 8*y^2 - 7*x + 8*y = 0, the corresponding values of x being A253446. %H A253447 Colin Barker, <a href="/A253447/b253447.txt">Table of n, a(n) for n = 1..678</a> %H A253447 Giovanni Lucca, <a href="http://forumgeom.fau.edu/FG2016volume16/FG2016volume16.pdf#page=423">Circle Chains Inscribed in Symmetrical Lenses and Integer Sequences</a>, Forum Geometricorum, Volume 16 (2016) 419-427. %H A253447 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (31,-31,1). %F A253447 a(n) = 31*a(n-1)-31*a(n-2)+a(n-3). %F A253447 G.f.: -x*(x^2-16*x+1) / ((x-1)*(x^2-30*x+1)). %F A253447 a(n) = (8+(4+sqrt(14))*(15+4*sqrt(14))^(-n)-(-4+sqrt(14))*(15+4*sqrt(14))^n)/16. - _Colin Barker_, Mar 03 2016 %e A253447 15 is in the sequence because the 15th centered octagonal number is 841, which is also the 16th centered heptagonal number. %o A253447 (PARI) Vec(-x*(x^2-16*x+1)/((x-1)*(x^2-30*x+1)) + O(x^100)) %Y A253447 Cf. A016754, A069099, A253446, A253514. %K A253447 nonn,easy %O A253447 1,2 %A A253447 _Colin Barker_, Jan 01 2015