cp's OEIS Frontend

A166964 Number of n-colorings of the Errera graph.

%I A166964 #23 Feb 16 2025 08:33:11
%S A166964 0,0,0,0,960,4669200,1342968480,96351366720,2967164565120,
%T A166964 51747096270240,600189633086400,5123179804311360,34443698001387840,
%U A166964 191288688014664240,908558913657114720,3788089202221833600,14145018198653072640,48056437943548695360
%N A166964 Number of n-colorings of the Errera graph.
%C A166964 The Errera graph is a planar graph on 17 vertices and 45 edges with chromatic number 4.
%H A166964 Alois P. Heinz, <a href="/A166964/b166964.txt">Table of n, a(n) for n = 0..1000</a>
%H A166964 Marc Timme, Frank van Bussel, Denny Fliegner, and Sebastian Stolzenberg, <a href="http://dx.doi.org/10.1088/1367-2630/11/2/023001">Counting complex disordered states by efficient pattern matching: chromatic polynomials and Potts partition functions</a>, New J. Phys. 11 023001 (2009).
%H A166964 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ErreraGraph.html">Errera Graph</a>.
%H A166964 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>.
%H A166964 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (18, -153, 816, -3060, 8568, -18564, 31824, -43758, 48620, -43758, 31824, -18564, 8568, -3060, 816, -153, 18, -1).
%F A166964 a(n) = n^17 - 45*n^16 + ... (see Maple program).
%p A166964 a:= n-> n^17 -45*n^16 +960*n^15 -12900*n^14 +122327*n^13 -868834*n^12 +4785355*n^11 -20863215*n^10 +72791543*n^9 -203886157*n^8 +456534224*n^7 -807157880*n^6 +1101393064*n^5 -1116652249*n^4 +788961246*n^3 -344673280*n^2 +69525840*n:
%p A166964 seq(a(n), n=0..20);
%t A166964 a[n_] := n^17 - 45*n^16 + 960*n^15 - 12900*n^14 + 122327*n^13 - 868834*n^12 + 4785355*n^11 - 20863215*n^10 + 72791543*n^9 - 203886157*n^8 + 456534224*n^7 - 807157880*n^6 + 1101393064*n^5 - 1116652249*n^4 + 788961246*n^3 - 344673280*n^2 + 69525840*n;  Table[a[n], {n, 0, 10}] (* _G. C. Greubel_, May 29 2016 *)
%K A166964 nonn,easy
%O A166964 0,5
%A A166964 _Alois P. Heinz_, Oct 25 2009