|
|
A158344
|
|
Number of n-colorings of the Folkman Graph.
|
|
2
|
|
|
0, 0, 2, 18648, 45718044, 22839203000, 3322954977390, 196998967990272, 6100155102337688, 116724860607772944, 1546577491554833850, 15357702814950199880, 120959689823708363892, 787872289121987384328, 4380104959751908990694, 21297248362250478298800
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
The Folkman Graph has 20 vertices and 40 edges. It is the semi-symmetric graph with the fewest possible vertices.
|
|
LINKS
|
Timme, Marc; van Bussel, Frank; Fliegner, Denny; Stolzenberg, Sebastian (2009) "Counting complex disordered states by efficient pattern matching: chromatic polynomials and Potts partition functions", New J. Phys. 11 023001, doi: 10.1088/1367-2630/11/2/023001.
Index entries for linear recurrences with constant coefficients, signature (21, -210, 1330, -5985, 20349, -54264, 116280, -203490, 293930, -352716, 352716, -293930, 203490, -116280, 54264, -20349, 5985, -1330, 210, -21, 1).
|
|
FORMULA
|
a(n) = n^20 -40*n^19 + ... (see Maple program).
|
|
MAPLE
|
a:= n-> n^20 -40*n^19 +780*n^18 -9850*n^17 +90300*n^16 -638683*n^15 +3616080*n^14 -16782060*n^13 +64834630*n^12 -210500726*n^11 +577081604*n^10 -1336290915*n^9 +2602586625*n^8 -4222943355*n^7 +5616671680*n^6 -5968728608*n^5 +4868919865*n^4 -2855170950*n^3 +1066503307*n^2 -189239685*n:
seq(a(n), n=0..30);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|