cp's OEIS Frontend

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.

A200999 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.

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