A173710 Number of n-colorings of the Truncated Icosahedral Graph (Buckminsterfullerene Graph).

0, 0, 0, 4730288584320, 7069863662920679029221840, 1600833675669527372906737847234640, 3607392051635570971851531552033867919920, 476173191496426716314609213751835468517640720, 9214454846080323862466512527969533680469693123040

Offset: 0

Author

Alois P. Heinz, Nov 25 2010

Keywords

• nonn
• easy

Comments

The Truncated Icosahedral Graph has 60 nodes and 90 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.
• Eric Weisstein's World of Mathematics, Truncated Icosahedral Graph
• Wikipedia, Buckminsterfullerene
• Wikipedia, Truncated icosahedron
• Index entries for linear recurrences with constant coefficients, signature (61, -1830, 35990, -521855, 5949147, -55525372, 436270780, -2944827765, 17341763505, -90177170226, 418094152866, -1742058970275, 6566222272575, -22512762077400, 70539987842520, -202802465047245, 536830054536825, -1312251244423350, 2969831763694950, -6236646703759395, 12176310231149295, -22138745874816900, 37539612570341700, -59437719903041025, 87967825456500717, -121801604478231762, 157890968768078210, -191724747789809255, 218169540588403635, -232714176627630544, 232714176627630544, -218169540588403635, 191724747789809255, -157890968768078210, 121801604478231762, -87967825456500717, 59437719903041025, -37539612570341700, 22138745874816900, -12176310231149295, 6236646703759395, -2969831763694950, 1312251244423350, -536830054536825, 202802465047245, -70539987842520, 22512762077400, -6566222272575, 1742058970275, -418094152866, 90177170226, -17341763505, 2944827765, -436270780, 55525372, -5949147, 521855, -35990, 1830, -61, 1).

Crossrefs

Cf. A173705.

Programs

Maple

a:= n-> n^60 -90*n^59 +4005*n^58 -117480*n^57 +2555178*n^56 -43948216*n^55 [phone]*n^54 -7470076080*n^53 [phone]*n^52 -705794122958*n^51 [phone]*n^50 -41531475565130*n^49 [phone]*n^48 -1636906872884846*n^47 +8987923959372248*n^46 -45439850403582388*n^45 +212408918047206910*n^44 -921385538493380470*n^43 +3720619807069084604*n^42 -14024779187530233492*n^41
+49469651965066308909*n^40 -163633523117076857150*n^39 +508526841251772505638*n^38 -1487246856610831165182*n^37 +4099316537037158137551*n^36 -10662312377979200024192*n^35 +26198885531512430256440*n^34 -60872164258005163891048*n^33 +133847345021136234242787*n^32 -278706700332950912182478*n^31 +549878457860549069326076*n^30 -1028366308985215091666200*n^29 +1823547468622777997253242*n^28
-3066527365445816141902890*n^27 +4890520241242906191260322*n^26 -7396112277649732169713915*n^25 +10604622335494603801764126*n^24 -14410226451738975550233448*n^23 +18548267973329701722804123*n^22 -22599125270247643754403309*n^21 +26040611686995159246437196*n^20 -28346723254600246052342657*n^19 +29111044852232535929992609*n^18 -28157742221447853779944789*n^17 +25600595332414641354114944*n^16
-21824956195231415021694903*n^15 +17394595782497717853665150*n^14 -12913641300543584608175056*n^13 +8890033214947388390603558*n^12 -5643531045178823946756226*n^11 +3280540608384297010799755*n^10 -1730696947367076894316252*n^9 +819222671768491649284049*n^8 -342742027300432825029400*n^7 +124211147299632169743001*n^6 -37914778572755712686607*n^5 +9356112463643258845408*n^4
-1748844869052231366256*n^3 +219901173144505099314*n^2 -13932794681567505492*n: seq(a(n), n=0..10);

Formula

a(n) = n^60 -90*n^59 + ... (see Maple program).