%I #19 Aug 16 2015 12:03:56

%S 1,651,180868051,95317119801,26472137730696901,13950766352135999751,

%T 3874504486629442861646551,2041856512426320950146560501,

%U 567078683619272811125915867157001,298849390212849227278846377616002051,82998544594567922836927983404875025948251

%N 9-gonal pentagonal numbers.

%C From _Ant King_, Dec 20 2011: (Start)

%C lim(n->Infinity, a(2n+1)/a(2n))=1/2*(277727+60605*sqrt(21)).

%C lim(n->Infinity, a(2n)/a(2n-1))=1/2*(527+115*sqrt(21)).

%C (End)

%H Colin Barker, <a href="/A048915/b048915.txt">Table of n, a(n) for n = 1..246</a>

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

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,146361602,-146361602,-1,1).

%F From _Ant King_, Dec 20 2011: (Start)

%F a(n) = 146361602*a(n-2)-a(n-4)+35719200.

%F a(n) = a(n-1)+146361602*a(n-2)-146361602*a(n-3)-a(n-4)+a(n-5).

%F a(n) = 1/336*((25+4*sqrt(21))*(5-sqrt(21)*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(4n-4)+ (25-4*sqrt(21))*(5+sqrt(21)*(-1)^n)*(2*sqrt(7)-3*sqrt(3))^(4n-4)-82).

%F a(n) = floor(1/336*(25+4*sqrt(21))*(5-sqrt(21)*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(4n-4)).

%F G.f.: x*(1+650*x+34505798*x^2+1210450*x^3+2301*x^4) / ((1-x)*(1-12098*x+x^2)*(1+12098*x+x^2)).

%F (End)

%t LinearRecurrence[{1, 146361602, -146361602, -1, 1}, {1, 651, 180868051, 95317119801, 26472137730696901}, 9] (* _Ant King_, Dec 20 2011 *)

%o (PARI) Vec(x*(1+650*x+34505798*x^2+1210450*x^3+2301*x^4)/((1-x)*(1-12098*x+x^2)*(1+12098*x+x^2)) + O(x^20)) \\ _Colin Barker_, Jun 22 2015

%Y Cf. A048913, A048914.

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_