A068245 1/6 the number of colorings of a 4 X 4 rhombic- or staggered- hexagonal array with n colors.

1, 7616, 5141250, 552093440, 20631905875, 395001645696, 4771909547076, 41190314035200, 275192443300005, 1502690499112000, 6971521964029766, 28275884687022336, 102456840191225975, 337289521082456320, 1022310183284613000, 2883605488481550336, 7636012822945480521

Offset

3,2

Comments

Numbers for rhombic- and staggered- hexagonal arrays differ above 4 X 4.

Links

Alois P. Heinz, Table of n, a(n) for n = 3..1000

Formula

From Alois P. Heinz, May 02 2012: (Start)

G.f.: -(7926831*x^13 +710120929*x^12 +16477733814*x^11 +144915014346*x^10 +569769493505*x^9 +1086745824783*x^8 +1040642122932*x^7 +499586289612*x^6 +115866023553*x^5 +11940350895*x^4 +465727286*x^3 +5011914*x^2 +7599*x+1) *x^3 / (x-1)^17.

a(n) = (n^16 -33*n^15 +510*n^14 -4898*n^13 +32703*n^12 -160859*n^11 +602408*n^10 -1749715*n^9 +3975561*n^8 -7068408*n^7 +9755858*n^6 -10265148*n^5 +7968348*n^4 -4304712*n^3 +1445104*n^2 -226720*n)/6. (End)

Maple

a:= n-> (-226720+ (1445104+ (-4304712+ (7968348+ (-10265148+ (9755858+ (-7068408+ (3975561+ (-1749715+ (602408+ (-160859+ (32703+ (-4898+ (510+ (-33+n)*n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n/6:
seq(a(n), n=3..40); #  Alois P. Heinz, May 02 2012

Prog

(Magma) [(n^11 -26*n^10 +310*n^9 -2240*n^8 +10915*n^7 -37726*n^6 +94576*n^5 -172395*n^4 +224588*n^3 -199854*n^2 +109788*n -28340)*n *(n-1)*(n-2)^3/6: n in [3..19]]; // Bruno Berselli, May 03 2012

Crossrefs

Cf. A068239-A068305, A000332, A002417, A027441, A212162, A212163.

Sequence in context: A233881 A031854 A253041 * A189551 A235907 A252968

Adjacent sequences: A068242 A068243 A068244 * A068246 A068247 A068248

Keyword

nonn,easy

Author

R. H. Hardin, Feb 24 2002

Extensions

Extended beyond a(15) by Alois P. Heinz, May 02 2012

Status

approved