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%I #20 Mar 02 2016 09:16:29
%S 0,28,5460,1059240,205487128,39863443620,7733302575180,
%T 1500220836141328,291035108908842480,56459310907479299820,
%U 10952815280942075322628,2124789705191855133290040,412198249991938953782945160,79964335708730965178758071028
%N Triangular numbers, T(m), that are four-thirds of another triangular number; T(m) such that 3*T(m) = 4*T(k) for some k.
%C Numbers h such that 6*h+1 and 8*h+1 are both squares. [_Bruno Berselli_, Jul 07 2014]
%H Colin Barker, <a href="/A200999/b200999.txt">Table of n, a(n) for n = 0..400</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (195,-195,1).
%F For n>1, a(n) = 194*a(n-1) - a (n-2) + 28. See A200998 for generalization.
%F From _Colin Barker_, Mar 02 2016: (Start)
%F a(n) = ((97+56*sqrt(3))^(-n)*(-1+(97+56*sqrt(3))^n)*(-7+4*sqrt(3)+(7+4*sqrt(3))*(97+56*sqrt(3))^n))/96.
%F a(n) = 195*a(n-1)-195*a(n-2)+a(n-3) for n>2.
%F G.f.: 28*x / ((1-x)*(1-194*x+x^2)).
%F (End)
%e 3*0 = 4*0.
%e 3*28 = 4*21.
%e 3*5640 = 4*4095.
%e 3*1059240 = 4*794430.
%t LinearRecurrence[{195, -195, 1}, {0, 28, 5460}, 20] (* _T. D. Noe_, Feb 15 2012 *)
%o (PARI) concat(0, Vec(28*x/((1-x)*(1-194*x+x^2)) + O(x^15))) \\ _Colin Barker_, Mar 02 2016
%Y Cf. A200994, A245031.
%K nonn,easy
%O 0,2
%A _Charlie Marion_, Feb 15 2012
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