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%I #40 Dec 30 2023 23:46:33
%S 0,1,20,285,3976,55385,771420,10744501,149651600,2084377905,
%T 29031639076,404358569165,5631988329240,78443478040201,
%U 1092576704233580,15217630381229925,211954248632985376,2952141850480565345,41118031658094929460,572700301362848447101
%N Indices of triangular numbers which are also pentagonal.
%H Colin Barker, <a href="/A046175/b046175.txt">Table of n, a(n) for n = 0..874</a>
%H W. Sierpiński, <a href="http://www.ams.org/mathscinet-getitem?mr=171743">Sur les nombres pentagonaux</a>, Bull. Soc. Roy. Sci. Liege 33 (1964) 513-517
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PentagonalTriangularNumber.html">Pentagonal Triangular Number</a>, MathWorld
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (15,-15,1).
%F From _Warut Roonguthai_, Jan 05 2001: (Start)
%F a(n) = 14*a(n-1) - a(n-2) + 6.
%F G.f.: x*(1+5*x)/((1-x)*(1-14*x+x^2)). (End)
%F a(n+1) = 7*a(n) + 3 + 2*sqrt(12*a(n)^2 + 12*a(n) + 1). - _Richard Choulet_, Sep 19 2007
%F a(n+1) = 15*a(n)-15*a(n-1)+ a(n-2) with a(1)=1, a(2)=20, a(3)=285. - _Sture Sjöstedt_, May 29 2009
%t LinearRecurrence[{15,-15,1},{0,1,20},20] (* _Harvey P. Dale_, Sep 10 2021 *)
%o (PARI) concat(0, Vec(-x*(5*x+1)/((x-1)*(x^2-14*x+1)) + O(x^50))) \\ _Colin Barker_, Jun 23 2015
%Y Cf. A014979, A046174, A001834.
%K nonn,easy
%O 0,3
%A _Eric W. Weisstein_
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