%I #26 Apr 04 2024 04:22:05
%S 3,280,5265,47040,271250,1170288,4105710,12334080,32837805,79365000,
%T 177200023,370319040,731732820,1377981920,2488927500,4334174208,
%U 7307669895,11972250360,19116135885,29823640000,45562619718,68291480400,100588847450,145809331200
%N 1/24 the number of colorings of a 3 X 3 octagonal array with n colors.
%H Alois P. Heinz, <a href="/A068250/b068250.txt">Table of n, a(n) for n = 4..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F From _Alois P. Heinz_, May 04 2012: (Start)
%F G.f.: (832*x^5+4805*x^4+6630*x^3+2600*x^2+250*x+3)*x^4 / (x-1)^10.
%F a(n) = (n^9 -20*n^8 +174*n^7 -859*n^6 +2627*n^5 -5082*n^4 +6048*n^3 -4023*n^2 +1134*n)/24. (End)
%p a:= n-> (n-2)*(n-1)*(n^2-5*n+7)*(n-3)^4*n/24:
%p seq(a(n), n=4..40); # _Alois P. Heinz_, May 04 2012
%o (Magma) [n*(n-3)^4*(n^4-8*n^3+24*n^2-31*n+14)/24: n in [4..27]]; // _Bruno Berselli_, May 04 2012
%Y Cf. A068239-A068305, A000332, A002417, A027441, A212208, A212209.
%K nonn,easy
%O 4,1
%A _R. H. Hardin_, Feb 24 2002