OFFSET
0,4
COMMENTS
The 3 X 3 X 3 triangular grid has 3 rows with k vertices in row k. Each vertex is connected to the neighbors in the same row and up to two vertices in each of the neighboring rows. The graph has 6 vertices and 9 edges altogether.
REFERENCES
Burkard Polster and Marty Ross, Math Goes to the Movies, The Johns Hopkins University Press, Baltimore, 2013, ยง1.10 Mathematics: Graph Theory 3, pp. 16-17.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Wikipedia, Chromatic polynomial
Wikipedia, Triangular grid graph
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = n*(n-1)*(n-2)^4.
G.f.: 6*x^3*(1 + 25*x + 67*x^2 + 27*x^3) / (1-x)^7.
a(0)=0, a(1)=0, a(2)=0, a(3)=6, a(4)=192, a(5)=1620, a(6)=7680, a(n) = 7*a(n-1) -21*a(n-2) +35*a(n-3) -35*a(n-4) +21*a(n-5) -7*a(n-6) +a(n-7). - Harvey P. Dale, Dec 10 2011
MAPLE
a:= n-> n*(n-1)*(n-2)^4: seq(a(n), n=0..30);
MATHEMATICA
Table[n(n-1)(n-2)^4, {n, 0, 30}] (* or *) LinearRecurrence[ {7, -21, 35, -35, 21, -7, 1}, {0, 0, 0, 6, 192, 1620, 7680}, 30] (* Harvey P. Dale, Dec 10 2011 *)
PROG
(PARI) a(n)=n*(n-1)*(n-2)^4 \\ Charles R Greathouse IV, Jun 22 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Dec 02 2010
STATUS
approved