A068251 1/24 the number of colorings of a 4 X 4 octagonal array with n colors.

7, 38960, 11043135, 715016960, 19498281250, 301435761312, 3120392830170, 23965758136320, 146127409139745, 741378459250000, 3237913809747617, 12485709312410880, 43342515673364180, 137520873034108480, 403684061693062500, 1107133265664540672, 2859892150083272715

Offset: 4

Author

R. H. Hardin, Feb 24 2002

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..1000

Crossrefs

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

Programs

Maple

a:= n-> (-5709042+ (30931875+ (-77301243+ (118705077+ (-125639547+ (97292827+ (-57031153+ (25795983+ (-9084089+ (2491825+ (-528254+ (85011+ (-10054+ (825+ (-42+n)*n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n)*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.: -(22941952*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 [phone]*x^2 +38841*x +7)*x^4 / (x-1)^17.

a(n) = (n^16 -42*n^15 +825*n^14 -10054*n^13 +85011*n^12 -528254*n^11 +2491825*n^10 -9084089*n^9 [phone]*n^8 -57031153*n^7 [phone]*n^6 -125639547*n^5 [phone]*n^4 -77301243*n^3 [phone]*n^2 -5709042*n)/24. (End)