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A158348 Number of n-colorings of the Hypercube Graph Q4.

%I A158348 #22 Jul 06 2025 18:58:45
%S A158348 0,0,2,2970,1321860,187430900,10199069190,269591166222,4221404762120,
%T A158348 44876701584360,355148098691850,2230178955481730,11630998385335692,
%U A158348 52097117078470620,205557074788375310,728566149746575350,2355657801908655120,7034253747275048912,19594719516430397970
%N A158348 Number of n-colorings of the Hypercube Graph Q4.
%C A158348 The Hypercube Graph Q4 has 16 vertices and 32 edges.
%C A158348 All terms are even.
%H A158348 Alois P. Heinz, <a href="/A158348/b158348.txt">Table of n, a(n) for n = 0..1000</a>
%H A158348 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 A158348 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>
%H A158348 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>
%H A158348 <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 A158348 a(n) = n^16 -32*n^15 + ... (see Maple program).
%p A158348 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 A158348 seq(a(n), n=0..20);
%Y A158348 Cf. A140986, A380589.
%Y A158348 Column k=4 of A342128.
%K A158348 nonn,easy
%O A158348 0,3
%A A158348 _Alois P. Heinz_, Mar 16 2009