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 A274832 #16 Oct 21 2024 08:59:38
%S A274832 0,27,297,24570,267030,22064157,239792967,19813588740,215333817660,
%T A274832 17792580624687,193369528466037,15977717587380510,173645621228683890,
%U A274832 14347972600887073617,155933574493829667507,12884463417879004727880,140028176249837812737720
%N A274832 Values of n such that 2*n+1 and 7*n+1 are both triangular numbers (A000217).
%C A274832 Intersection of A074377 and A274830.
%H A274832 Colin Barker, <a href="/A274832/b274832.txt">Table of n, a(n) for n = 1..650</a>
%H A274832 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,898,-898,-1,1).
%F A274832 G.f.: 27*x^2*(1+10*x+x^2) / ((1-x)*(1-30*x+x^2)*(1+30*x+x^2)).
%e A274832 27 is in the sequence because 2*27+1 = 55, 7*27+1 = 190, and 55 and 190 are both triangular numbers.
%t A274832 LinearRecurrence[{1, 898, -898, -1, 1}, {0, 27, 297, 24570, 267030}, 20] (* _Paolo Xausa_, Oct 21 2024 *)
%o A274832 (PARI) isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(7*n+1, 3)
%o A274832 (PARI) concat(0, Vec(27*x^2*(1+10*x+x^2)/((1-x)*(1-30*x+x^2)*(1+30*x+x^2)) + O(x^20)))
%Y A274832 Cf. A000217, A074377, A274830.
%Y A274832 Cf. A124174 (2*n+1 and 9*n+1), A274579 (2*n+1 and 5*n+1), A274603 (2*n+1 and 3*n+1), A274680 (2*n+1 and 4*n+1), A274756 (2*n+1 and 7*n+1).
%K A274832 nonn,easy
%O A274832 1,2
%A A274832 _Colin Barker_, Jul 08 2016