A158343 Number of n-colorings of the Great Rhombicuboctahedral Graph.

0, 0, 2, 99211884354, 128404924735509594684, 454361430700434252792759260, 49304046115345772654010126834750, 587577368663018907136035272423004222, 1542698164185222733139192724703158049304, 1351870094632808306932934388395466991540824

Offset: 0

Author

Alois P. Heinz, Mar 16 2009

Keywords

• nonn
• easy

Comments

The Great Rhombicuboctahedral Graph has 48 vertices and 72 edges.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• 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: 10.1088/1367-2630/11/2/023001.
• Weisstein, Eric W. "Great Rhombicuboctahedral Graph".
• Weisstein, Eric W. "Chromatic Polynomial".
• Index entries for linear recurrences with constant coefficients, signature (49, -1176, 18424, -211876, 1906884, -13983816, 85900584, -450978066, 2054455634, -8217822536, 29135916264, -92263734836, 262596783764, -675248872536, 1575580702584, -3348108992991, 6499270398159, -11554258485616, 18851684897584, -28277527346376, 39049918716424, -49699896548176, 58343356817424, -63205303218876, 63205303218876, -58343356817424, 49699896548176, -39049918716424, 28277527346376, -18851684897584, 11554258485616, -6499270398159, 3348108992991, -1575580702584, 675248872536, -262596783764, 92263734836, -29135916264, 8217822536, -2054455634, 450978066, -85900584, 13983816, -1906884, 211876, -18424, 1176, -49, 1).

Programs

Maple

a:= n-> n^48 -72*n^47 +2556*n^46 -59628*n^45 +1027962*n^44 -13963384*n^43 [phone]*n^42 -1462722354*n^41 [phone]*n^40 -83671357220*n^39 [phone]*n^38 -2921738977412*n^37 [phone]*n^36 -66826405863356*n^35 [phone]*n^34 -1050146773509960*n^33 +3656254498423918*n^32 -11728007823709952*n^31 +34755565384722662*n^30 -95382143564487362*n^29 +242898674702061819*n^28 -574951784922236576*n^27 +1266754599120775627*n^26 -2600750916486764078*n^25 +4980027914010487395*n^24
-8899566732232426920*n^23 +14848595452990189925*n^22 -23134202360563757120*n^21 +33654620125551260783*n^20 -45699744902488727526*n^19 +57889556263321349095*n^18 -68345464733552018627*n^17 +75109741829991047501*n^16 -76707186919739116852*n^15 +72642495050235566549*n^14 -63614601332090693546*n^13 +51332734030165204034*n^12 -37995071799236906932*n^11 +25644857441690560749*n^10 -15662964316212708644*n^9 +8568850073632256499*n^8 -4141689518405172628*n^7 +1735425596156145573*n^6 -613608780402588056*n^5 +175859991682860459*n^4 -38297031056003649*n^3 +5628146663027689*n^2 -417945559511493*n: seq(a(n), n=0..20);

Formula

a(n) = n^48 -72*n^47 + ... (see Maple program).