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%I #14 Aug 16 2015 12:04:01
%S 6,105,58311,1008910,559902916,9687554415,5376187741821,
%T 93019896484620,51622154137063026,893177036357767525,
%U 495675918647891434531,8576285810087387291130,4759480119234899417304336,82349495455282056411663435,45700527609217585557064800441
%N Positive triangular numbers (A000217) that are pentagonal numbers (A000326) divided by 2.
%C Intersection of A000217 and A193866 (even pentagonal numbers divided by 2). - _Michel Marcus_, Jun 20 2015
%H Colin Barker, <a href="/A259156/b259156.txt">Table of n, a(n) for n = 1..502</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,9602,-9602,-1,1).
%F G.f.: -x*(x^3+594*x^2+99*x+6) / ((x-1)*(x^2-98*x+1)*(x^2+98*x+1)).
%e 6 is in the sequence because 6 is the 3rd triangular number, and 2*6 is the 3rd pentagonal number.
%t LinearRecurrence[{1, 9602, -9602, -1, 1}, {6, 105, 58311, 1008910, 559902916}, 20] (* _Vincenzo Librandi_, Jun 20 2015 *)
%o (PARI) Vec(-x*(x^3+594*x^2+99*x+6)/((x-1)*(x^2-98*x+1)*(x^2+98*x+1)) + O(x^20))
%Y Cf. A000217, A000326, A193866, A259157-A259167.
%K nonn,easy
%O 1,1
%A _Colin Barker_, Jun 19 2015
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