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%I #23 Sep 08 2022 08:44:50
%S 0,24,46,154,204,396,474,750,856,1216,1350,1794,1956,2484,2674,3286,
%T 3504,4200,4446,5226,5500,6364,6666,7614,7944,8976,9334,10450,10836,
%U 12036,12450,13734,14176,15544,16014,17466,17964,19500,20026,21646,22200,23904
%N Even 9-gonal (or enneagonal) numbers.
%H Vincenzo Librandi, <a href="/A028992/b028992.txt">Table of n, a(n) for n = 0..10000</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) = (1/2)*(28*(n-1)^2 + 60*(n-1) + 33 + (14*(n-1)+15)*(-1)^(n-1)).
%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.: -2*x*(3*x^3+30*x^2+11*x+12) / ((x-1)^3*(x+1)^2). - _Colin Barker_, May 30 2015
%o (Magma) [(1/2)*(28*(n-1)^2 + 60*(n-1) + 33 + (14*(n-1)+15)*(-1)^(n-1)): n in [0..40]]; // _Vincenzo Librandi_, Aug 19 2011
%o (PARI) concat(0, Vec(-2*x*(3*x^3+30*x^2+11*x+12)/((x-1)^3*(x+1)^2) + O(x^100))) \\ _Colin Barker_, May 30 2015
%Y Cf. A001106.
%Y Cf. A014642, A028991, A028994.
%K nonn,easy
%O 0,2
%A _Patrick De Geest_
%E 0 inserted, offset and formula corrected by _Omar E. Pol_, Aug 19 2011
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