A158344 Number of n-colorings of the Folkman Graph.

0, 0, 2, 18648, 45718044, 22839203000, 3322954977390, 196998967990272, 6100155102337688, 116724860607772944, 1546577491554833850, 15357702814950199880, 120959689823708363892, 787872289121987384328, 4380104959751908990694, 21297248362250478298800

Offset: 0

Author

Alois P. Heinz, Mar 16 2009

Keywords

• nonn
• easy

Comments

The Folkman Graph has 20 vertices and 40 edges. It is the semi-symmetric graph with the fewest possible vertices.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Folkman, Jon, Regular line-symmetric graphs, Journal of Combinatorial Theory, 3 (3) (1967), 215-232.
• 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.
• Eric Weisstein's World of Mathematics, Folkman Graph
• Eric Weisstein's World of Mathematics, Chromatic Polynomial
• Wikipedia, Folkman graph
• 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).

Programs

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 [phone]*n^12 -210500726*n^11 [phone]*n^10 -1336290915*n^9 [phone]*n^8 -4222943355*n^7 [phone]*n^6 -5968728608*n^5 [phone]*n^4 -2855170950*n^3 [phone]*n^2 -189239685*n:
seq(a(n), n=0..30);

Formula

a(n) = n^20 -40*n^19 + ... (see Maple program).