A068240 1/2 the number of colorings of a 4 X 4 square array with n colors.

1, 3906, 3000366, 414425080, 19064362455, 428429377026, 5861180425996, 55823546748096, 403783634784285, 2353615149832210, 11531349080992026, 48981767072238936, 184656623163700051, 629125059062885490, 1964980839044519640, 5691311662142685376

Offset: 2

Author

R. H. Hardin, Feb 24 2002

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A068239-A068305, A000332, A002417, A027441, A182368, A182406.

Programs

Maple

a:= n-> n*(n-1)*(17493+(-94782+(251492+(-430857+(529770+(-492434 +(355622+(-202160+(90723+(-31939+(8675+(-1762+(253 +(-23+n)*n)*n) *n)*n)*n)*n) *n)*n) *n)*n) *n)*n)*n) /2:
seq(a(n), n=2..30); # Alois P. Heinz, Apr 27 2012

Formula

From Alois P. Heinz, Apr 27 2012 (Start)

G.f.: -(2507986*x^14 [phone]*x^13 [phone]*x^12 [phone]*x^11 [phone]*x^10 [phone]*x^9 [phone]*x^8 [phone]*x^7 [phone]*x^6 [phone]*x^5 [phone]*x^4 [phone]*x^3 +2934100*x^2 +3889*x+1)*x^2 / (x-1)^17.

a(n) = n*(n-1)*(n^14 -23*n^13 +253*n^12 -1762*n^11 +8675*n^10 -31939*n^9 +90723*n^8 -202160*n^7 +355622*n^6 -492434*n^5 +529770*n^4 -430857*n^3 +251492*n^2 -94782*n +17493)/2.

(End)