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Number of n-colorings of the Hypercube Graph Q4.
7

%I #15 Jan 21 2024 09:56:59

%S 0,0,2,2970,1321860,187430900,10199069190,269591166222,4221404762120,

%T 44876701584360,355148098691850,2230178955481730,11630998385335692,

%U 52097117078470620,205557074788375310,728566149746575350,2355657801908655120,7034253747275048912

%N Number of n-colorings of the Hypercube Graph Q4.

%C The Hypercube Graph Q4 has 16 vertices and 32 edges.

%C All terms are even.

%H Alois P. Heinz, <a href="/A158348/b158348.txt">Table of n, a(n) for n = 0..1000</a>

%H 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: <a href="http://dx.doi.org/10.1088/1367-2630/11/2/023001">10.1088/1367-2630/11/2/023001</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).

%F a(n) = n^16 -32*n^15 + ... (see Maple program).

%p a:= n-> n^16 -32*n^15 +496*n^14 -4936*n^13 +35264*n^12 -191600*n^11 +818036*n^10 -2794896*n^9 +7701952*n^8 -17100952*n^7 +30276984*n^6 -41821924*n^5 +43389646*n^4 -31680240*n^3 +14412776*n^2 -3040575*n:

%p seq(a(n), n=0..20);

%Y Cf. A140986.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Mar 16 2009