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A068239
1/2 the number of colorings of a 3 X 3 square array with n colors.
68
1, 123, 4806, 71410, 583455, 3232341, 13675228, 47502036, 141991245, 377162335, 910842306, 2033854758, 4253012491, 8411348505, 15856955640, 28673921896, 49991146713, 84387303171, 138412872190, 221253017370, 345558093111, 528471784093, 792890261076, 1168989306300, 1696060111525
OFFSET
2,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
From Alois P. Heinz, Apr 27 2012: (Start)
G.f.: x^2*(1199*x^7 +16567*x^6 +60099*x^5 +71075*x^4 +28765*x^3 +3621*x^2 +113*x+1) / (x-1)^10.
a(n) = (79*n -323*n^2 +594*n^3 -648*n^4 +459*n^5 -216*n^6 +66*n^7 -12*n^8 +n^9) / 2. (End)
MAPLE
a:= n-> (79+(-323+(594+(-648+(459+(-216+(66+(-12+n)*n)*n) *n)*n)*n)*n)*n) *n/2:
seq(a(n), n=2..30); # Alois P. Heinz, Apr 27 2012
MATHEMATICA
A068239[n_] := (n - 1)*n*(n*(n*(n*(n*(n*((n - 11)*n + 55) - 161) + 298) - 350) + 244) - 79)/2;
Array[A068239, 25, 2] (* or *)
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 123, 4806, 71410, 583455, 3232341, 13675228, 47502036, 141991245, 377162335}, 25] (* Paolo Xausa, Apr 01 2026 *)
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Feb 24 2002
STATUS
approved