A068244 1/6 the number of colorings of a 3 X 3 rhombic- or staggered- hexagonal array with n colors.

1, 176, 5490, 65600, 455875, 2239776, 8647716, 27962880, 78920325, 200002000, 464447126, 1003294656, 2039332295, 3935444800, 7261533000, 12884914176, 22089914121, 36733221360, 59442494650, 93866696000, 144987663051, 219503536736, 326295822700, 476993088000

Offset: 3

Author

R. H. Hardin, Feb 24 2002

Keywords

• nonn

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

Crossrefs

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

Programs

Maple

a:= n-> (248 +(-1012 +(1786 +(-1791 +(1120 +(-448 +(112 +(-16+n)*n) *n) *n) *n) *n) *n) *n) *n/6:
seq(a(n), n=3..40);  #  Alois P. Heinz, May 02 2012

Formula

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

G.f.: (1089*x^6+10934*x^5+26015*x^4+18500*x^3+3775*x^2+166*x+1) / (x-1)^10*x^3.

a(n) = (n^9 -16*n^8 +112*n^7 -448*n^6 +1120*n^5 -1791*n^4 +1786*n^3 -1012*n^2 +248*n)/6. (End)