|
%I #14 Jan 31 2024 12:04:24
%S 0,0,2,356928,12099922596,49101447458720,32837837611390230,
%T 6426553644633315312,533800370960514099848,23739442745823623206656,
%U 657668636438409768373290,12584142706200655870739360,178943783391165445637763372,1995231603312151326801233568
%N Number of n-colorings of the Deltoidal Icositetrahedral Graph.
%C The Deltoidal Icositetrahedral Graph has 26 vertices and 48 edges.
%H Alois P. Heinz, <a href="/A158346/b158346.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 Weisstein, Eric W. "<a href="http://mathworld.wolfram.com/DeltoidalIcositetrahedralGraph.html">Deltoidal Icositetrahedral Graph</a>".
%H Weisstein, Eric W. "<a href="http://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>".
%H <a href="/index/Rec#order_27">Index entries for linear recurrences with constant coefficients</a>, signature (27, -351, 2925, -17550, 80730, -296010, 888030, -2220075, 4686825, -8436285, 13037895, -17383860, 20058300, -20058300, 17383860, -13037895, 8436285, -4686825, 2220075, -888030, 296010, -80730, 17550, -2925, 351, -27, 1).
%F a(n) = n^26 -48*n^25 + ... (see Maple program).
%p a:= n-> n^26 -48*n^25 +1128*n^24 -17272*n^23 +193500*n^22 -1688536*n^21 +11930900*n^20 -70058175*n^19 +348177439*n^18 -1483953200*n^17 +5476121836*n^16 -17616949248*n^15 +49637181582*n^14 -122824349683*n^13 +267154252219*n^12 -510315163003*n^11 +853539489883*n^10 -1243277337267*n^9 +1563797242570*n^8 -1677188669554*n^7 +1505883391012*n^6 -1101833801576*n^5 +630811311156*n^4 -264660711615*n^3 +72176888542*n^2 -9563482591*n: seq(a(n), n=0..20);
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Mar 16 2009
|
