A068250 1/24 the number of colorings of a 3 X 3 octagonal array with n colors.
3, 280, 5265, 47040, 271250, 1170288, 4105710, 12334080, 32837805, 79365000, 177200023, 370319040, 731732820, 1377981920, 2488927500, 4334174208, 7307669895, 11972250360, 19116135885, 29823640000, 45562619718, 68291480400, 100588847450, 145809331200
Offset: 4
Links
- Alois P. Heinz, Table of n, a(n) for n = 4..1000
- Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
Programs
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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
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Maple
a:= n-> (n-2)*(n-1)*(n^2-5*n+7)*(n-3)^4*n/24: seq(a(n), n=4..40); # Alois P. Heinz, May 04 2012
Formula
From Alois P. Heinz, May 04 2012: (Start)
G.f.: (832*x^5+4805*x^4+6630*x^3+2600*x^2+250*x+3)*x^4 / (x-1)^10.
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)