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1/24 the number of colorings of a 4 X 4 octagonal array with n colors.
2

%I #11 Aug 13 2013 19:44:09

%S 7,38960,11043135,715016960,19498281250,301435761312,3120392830170,

%T 23965758136320,146127409139745,741378459250000,3237913809747617,

%U 12485709312410880,43342515673364180,137520873034108480,403684061693062500,1107133265664540672,2859892150083272715

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

%H Alois P. Heinz, <a href="/A068251/b068251.txt">Table of n, a(n) for n = 4..1000</a>

%F From _Alois P. Heinz_, May 04 2012: (Start)

%F 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.

%F 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)

%p 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:

%p seq(a(n), n=4..40); # _Alois P. Heinz_, May 04 2012

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

%K nonn

%O 4,1

%A _R. H. Hardin_, Feb 24 2002