OFFSET
0,4
COMMENTS
The 5 X 5 X 5 triangular grid has 5 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 15 vertices and 30 edges altogether.
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 (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
FORMULA
a(n) = n*(n-1)*(n^9 -21*n^8 +198*n^7 -1102*n^6 +3999*n^5 -9840*n^4 +16475*n^3 -18177*n^2 +12056*n -3686)*(n-2)^4.
G.f.: 6*x^3*(1769985*x^12 +130265584*x^11 +2438678946*x^10 +17020599920*x^9 +51993920175*x^8 +74836435680*x^7 +51909140892*x^6 +17013829728*x^5 +2462276655*x^4 +136618800*x^3 +2186210*x^2 +5424*x +1)/(x-1)^16.
MAPLE
a:= n-> n^15 -30*n^14 +419*n^13 -3612*n^12 +21477*n^11 -93207*n^10 +304555*n^9 -761340*n^8 +1463473*n^7 -2152758*n^6 +2385118*n^5 -1929184*n^4 +1075936*n^3 -369824*n^2 +58976*n:
seq(a(n), n=0..30);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Dec 02 2010
STATUS
approved