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A158344
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Number of n-colorings of the Folkman Graph.
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2
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0, 0, 2, 18648, 45718044, 22839203000, 3322954977390, 196998967990272, 6100155102337688, 116724860607772944, 1546577491554833850, 15357702814950199880, 120959689823708363892, 787872289121987384328, 4380104959751908990694, 21297248362250478298800
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OFFSET
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0,3
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COMMENTS
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The Folkman Graph has 20 vertices and 40 edges. It is the semi-symmetric graph with the fewest possible vertices.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1000
Weisstein, Eric W. "Folkman Graph".
Weisstein, Eric W. "Chromatic Polynomial".
Wikipedia, Folkman graph
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.
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FORMULA
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a(n) = n^20 -40*n^19 + ... (see Maple program).
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MAPLE
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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);
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CROSSREFS
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Sequence in context: A151599 A159730 A214544 * A124364 A173156 A214598
Adjacent sequences: A158341 A158342 A158343 * A158345 A158346 A158347
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Mar 16 2009
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STATUS
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approved
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