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 A279043 #10 Dec 05 2016 05:27:45 %S A279043 63,12285,2383290,462346038,89692748145,17399930794155, %T A279043 3375496881317988,654828995044895580,127033449541828424595, %U A279043 24643834382119669475913,4780776836681674049902590,927446062481862646011626610,179919755344644671652205659813 %N A279043 Numbers k such that 3*k+1 and 4*k+1 are both triangular numbers (A000217). %H A279043 Colin Barker, <a href="/A279043/b279043.txt">Table of n, a(n) for n = 1..400</a> %H A279043 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (195,-195,1). %F A279043 a(n) = 195*a(n-1) - 195*a(n-2) + a(n-3) for n>3. %F A279043 G.f.: 63*x / ((1 - x)*(1 - 194*x + x^2)). %e A279043 63 is in the sequence because 3*63+1 = 190 and 4*63+1 = 253 are both triangular numbers. %o A279043 (PARI) Vec(63*x / ((1 - x)*(1 - 194*x + x^2)) + O(x^20)) %o A279043 (PARI) isok(k) = ispolygonal(3*k+1, 3) & ispolygonal(4*k+1, 3) %Y A279043 Cf. A000217, A274680. %K A279043 nonn,easy %O A279043 1,1 %A A279043 _Colin Barker_, Dec 04 2016