A048908 - OEIS

%I #25 Dec 30 2023 23:47:55

%S 1,25,406,6478,103249,1645513,26224966,417953950,6661038241,

%T 106158657913,1691877488374,26963881156078,429730221008881,

%U 6848719654986025,109149784258767526,1739547828485294398,27723615471505942849,441838299715609791193,7041689179978250716246

%N Indices of triangular numbers which are also 9-gonal.

%C lim( n -> Infinity , a(n)/a(n-1)) = 8 + 3*sqrt(7). - _Ant King_, Nov 03 2011

%H Colin Barker, <a href="/A048908/b048908.txt">Table of n, a(n) for n = 1..832</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NonagonalTriangularNumber.html">Nonagonal Triangular Number.</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (17,-17,1).

%F a(n+2) = 16*a(n+1)-a(n)+7, a(n+1) = 8*a(n)+3.5+1.5*(28*a(n)^2+28*a(n)+25)^0.5 - _Richard Choulet_, Sep 22 2007

%F G.f.: f(z) = a(1)*z+a(2)*z^2+... = (z+8z^2-2*z^3)/((1-z)*(1-16*z+z^2)) - _Richard Choulet_, Oct 09 2007

%F From _Ant King_, Nov 03 2011: (Start)

%F a(n) = 17*a(n-1) - 17*a(n-2) + a(n-3).

%F a(n) = floor(3/28*sqrt(7)*(3 - sqrt(7))*(8 + 3* sqrt(7))^n).

%F (End)

%t LinearRecurrence[{17, -17, 1}, {1, 25, 406}, 16]; (* _Ant King_, Nov 03 2011 *)

%o (PARI) Vec(x*(2*x^2-8*x-1)/((x-1)*(x^2-16*x+1)) + O(x^50)) \\ _Colin Barker_, Jun 22 2015

%Y Cf. A048907, A048909.

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_