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

4,1

Links

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

Formula

From Alois P. Heinz, May 04 2012: (Start)

G.f.: -(22941952*x^12 +1090564941*x^11 +15148153587*x^10 +85463400725*x^9 +223924774635*x^8 +289399790106*x^7 +187581268518*x^6 +59790636306*x^5 +8818383150*x^4 +532577465*x^3 +10381767*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 +25795983*n^8 -57031153*n^7 +97292827*n^6 -125639547*n^5 +118705077*n^4 -77301243*n^3 +30931875*n^2 -5709042*n)/24. (End)

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

Crossrefs

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

Sequence in context: A156169 A158898 A210846 * A033984 A368065 A348643

Adjacent sequences: A068248 A068249 A068250 * A068252 A068253 A068254

Keyword

nonn

Author

R. H. Hardin, Feb 24 2002

Status

approved