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%I #14 Dec 27 2020 14:41:19
%S 1,9,75,111,261,325,559,651,969,1089,1491,1639,2125,2301,2871,3075,
%T 3729,3961,4699,4959,5781,6069,6975,7291,8281,8625,9699,10071,11229,
%U 11629,12871,13299,14625,15081,16491,16975,18469,18981,20559,21099,22761,23329,25075
%N Odd 9-gonal (or enneagonal) numbers.
%H Colin Barker, <a href="/A028991/b028991.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NonagonalNumber.html">Nonagonal Number</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F a(n) = (28*n^2 + 4*n + 1 + (14*n+1)*(-1)^n)/2.
%F a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>4. - _Colin Barker_, May 30 2015
%F G.f.: -(19*x^4+20*x^3+64*x^2+8*x+1) / ((x-1)^3*(x+1)^2). - _Colin Barker_, May 30 2015
%t Select[PolygonalNumber[9,Range[100]],OddQ] (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[{1,2,-2,-1,1},{1,9,75,111,261},50] (* _Harvey P. Dale_, Dec 27 2020 *)
%o (PARI) Vec(-(19*x^4+20*x^3+64*x^2+8*x+1)/((x-1)^3*(x+1)^2) + O(x^100)) \\ _Colin Barker_, May 30 2015
%Y Cf. A001106, A028992.
%K nonn,easy
%O 0,2
%A _Patrick De Geest_