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 A253457 #15 Jun 13 2015 00:55:21 %S A253457 1,14,351,9100,236237,6133050,159223051,4133666264,107316099801, %T A253457 2786084928550,72330892042487,1877817108176100,48750913920536101, %U A253457 1265645944825762514,32858043651549289251,853043488995455758000,22146272670230300418737,574950045936992355129150 %N A253457 Indices of centered hexagonal numbers (A003215) which are also centered heptagonal numbers (A069099). %C A253457 Also positive integers x in the solutions to 6*x^2 - 7*y^2 - 6*x + 7*y = 0, the corresponding values of y being A253458. %H A253457 Colin Barker, <a href="/A253457/b253457.txt">Table of n, a(n) for n = 1..708</a> %H A253457 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (27,-27,1). %F A253457 a(n) = 27*a(n-1)-27*a(n-2)+a(n-3). %F A253457 G.f.: x*(13*x-1) / ((x-1)*(x^2-26*x+1)). %F A253457 a(n) = sqrt((-2-(13-2*sqrt(42))^n-(13+2*sqrt(42))^n)*(2-(13-2*sqrt(42))^(1+n)-(13+2*sqrt(42))^(1+n)))/(4*sqrt(6)). - _Gerry Martens_, Jun 04 2015 %e A253457 14 is in the sequence because the 14th centered hexagonal number is 547, which is also the 13th centered heptagonal number. %o A253457 (PARI) Vec(x*(13*x-1)/((x-1)*(x^2-26*x+1)) + O(x^100)) %Y A253457 Cf. A003215, A069099, A253458, A253546. %K A253457 nonn,easy %O A253457 1,2 %A A253457 _Colin Barker_, Jan 01 2015