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A223508 Petersen graph (3,1) coloring a rectangular array: number of 5Xn 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0 1

%I #4 Mar 21 2013 04:46:36

%S 1296,4913,266419,11148439,515473927,23328902821,1065016901935,

%T 48530437419865,2213179954647275,100913208621796747,

%U 4601629002961862345,209830596880154645775,9568174653385280051091,436303604544116583704607

%N Petersen graph (3,1) coloring a rectangular array: number of 5Xn 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0

%C Row 5 of A223504

%H R. H. Hardin, <a href="/A223508/b223508.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 71*a(n-1) -1025*a(n-2) -14582*a(n-3) +432132*a(n-4) -1235038*a(n-5) -44254492*a(n-6) +375953458*a(n-7) +1077097488*a(n-8) -24108628735*a(n-9) +43813966193*a(n-10) +660782580981*a(n-11) -3015474264116*a(n-12) -7468946258468*a(n-13) +72313665742943*a(n-14) -19748204982172*a(n-15) -929976166077118*a(n-16) +1623691507031261*a(n-17) +6877758733216211*a(n-18) -21986547259066956*a(n-19) -25977258135841984*a(n-20) +164780020970184872*a(n-21) -5445523483934936*a(n-22) -789421436773000211*a(n-23) +617827785709579554*a(n-24) +2499061275173634960*a(n-25) -3608966242372275158*a(n-26) -5054385737333805739*a(n-27) +11913328661514326768*a(n-28) +5266973549905528132*a(n-29) -26083920461220425468*a(n-30) +2323512355364237888*a(n-31) +39474091164345616200*a(n-32) -18570564930623297944*a(n-33) -41144392421727062733*a(n-34) +34192277387530560380*a(n-35) +27957670701203653789*a(n-36) -37366923751687843813*a(n-37) -9816688145756259804*a(n-38) +27153007122450867062*a(n-39) -1474941418773154672*a(n-40) -13352938311422813034*a(n-41) +3795826701250077433*a(n-42) +4315925800274009339*a(n-43) -2185410858126306921*a(n-44) -825385995637082366*a(n-45) +704751836109259081*a(n-46) +54959242071750150*a(n-47) -139309166655413192*a(n-48) +12738975912252902*a(n-49) +16584925179127396*a(n-50) -3592712328375964*a(n-51) -1071918437017524*a(n-52) +385473088083924*a(n-53) +24628625488560*a(n-54) -20197202519736*a(n-55) +763271541072*a(n-56) +473574597408*a(n-57) -42448453056*a(n-58) -3476245248*a(n-59) +407586816*a(n-60) for n>61

%e Some solutions for n=3

%e ..0..2..0....0..2..1....0..1..0....0..1..2....0..2..1....0..1..0....0..1..0

%e ..1..2..1....1..2..5....0..2..0....4..1..0....0..2..0....2..1..4....0..3..4

%e ..1..2..1....0..2..1....1..2..5....2..1..2....0..2..1....2..1..2....4..3..5

%e ..1..2..0....5..2..5....5..2..5....4..5..4....0..2..0....2..5..4....0..3..0

%e ..5..2..1....5..2..5....5..3..5....3..5..4....5..2..0....4..5..4....0..3..4

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 21 2013

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Last modified May 26 03:59 EDT 2024. Contains 372807 sequences. (Running on oeis4.)