%I #13 Apr 24 2021 09:31:19
%S 0,945,13167,35578242,495540990,1338951572595,18649189618605,
%T 50390103447476100,701843601611053692,1896381151803363988917,
%U 26413182084381205040235,71368408216577696911440390,994033693861758668873164410,2685878672926303893761783662455
%N Values of n such that 2*n+1 and 6*n+1 are both triangular numbers.
%C Intersection of A074377 and A274757.
%H Colin Barker, <a href="/A274756/b274756.txt">Table of n, a(n) for n = 1..400</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,37634,-37634,-1,1).
%F G.f.: 63*x^2*(15+194*x+15*x^2) / ((1-x)*(1-194*x+x^2)*(1+194*x+x^2)).
%F a(n) = a(n-1)+37634*a(n-2)-37634*a(n-3)-a(n-4)+a(n-5). - _Wesley Ivan Hurt_, Apr 24 2021
%e 945 is in the sequence because 2*945+1 = 1891, 6*945+1 = 5671, and 1891 and 5671 are both triangular numbers.
%o (PARI) isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(6*n+1, 3)
%o (PARI) concat(0, Vec(63*x^2*(15+194*x+15*x^2)/((1-x)*(1-194*x+x^2)*(1+194*x+x^2)) + O(x^20)))
%Y 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).
%K nonn,easy
%O 1,2
%A _Colin Barker_, Jul 04 2016