A173705 - OEIS

%I #23 May 30 2026 16:40:34

%S 0,0,0,175392,52636048080,236901615304560,136750498496102880,

%T 22791207032346814320,1646492374456377504672,65181439861421995954080,

%U 1639402077308605107361920,28932563258378720821964160,384247128673776043122297840,4041651944711085007033425552

%N Number of n-colorings of the 26-Fullerene Graph.

%C The 26-Fullerene Graph has 26 nodes and 39 edges.

%H Alois P. Heinz, <a href="/A173705/b173705.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="https://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="https://mathworld.wolfram.com/Fullerene.html">Fullerene</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Fullerene">Fullerene</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 -39*n^25 + ... (see Maple program).

%p a:= n-> n^26 -39*n^25 +741*n^24 -9139*n^23 +82239*n^22 -575334*n^21 +3255381*n^20 -15300714*n^19 +60877534*n^18 -207882246*n^17 +615460527*n^16 -1591600225*n^15 +3614170438*n^14 -7231312797*n^13 +12771014024*n^12 -19910338640*n^11 +27355291779*n^10 -32995251679*n^9 +34709871301*n^8 -31516729541*n^7 +24310852305*n^6 -15545301211*n^5 +7928693334*n^4 -3025373407*n^3 +766360836*n^2 -96255468*n: seq(a(n), n=0..15);

%Y Cf. A173710.

%K nonn,easy

%O 0,4

%A _Alois P. Heinz_, Nov 25 2010