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