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 A223560 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 or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0 1

%I #4 Mar 22 2013 05:40:40

%S 1296,19683,1172889,72906921,4715559621,308267930115,20248676896077,

%T 1332349841732589,87722782781246325,5776909246026951831,

%U 380457710460248943159,25056802652197918165101,1650241268196778787267997

%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 or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0

%C Row 5 of A223556

%H R. H. Hardin, <a href="/A223560/b223560.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 138*a(n-1) -6973*a(n-2) +184648*a(n-3) -2923158*a(n-4) +28742148*a(n-5) -164862328*a(n-6) +323303482*a(n-7) +2664572505*a(n-8) -23705019366*a(n-9) +69355645652*a(n-10) +70054378686*a(n-11) -1192186614062*a(n-12) +3436488705480*a(n-13) -144865949345*a(n-14) -25285605346206*a(n-15) +67796388682571*a(n-16) -36846019769990*a(n-17) -198206747323771*a(n-18) +539872407671898*a(n-19) -524423165469667*a(n-20) -173098284258962*a(n-21) +1095810256049880*a(n-22) -1391226239663130*a(n-23) +883819140137974*a(n-24) -205123488401360*a(n-25) -109599889287411*a(n-26) +100027213354804*a(n-27) -24361114004738*a(n-28) -4709924309874*a(n-29) +4076735604787*a(n-30) -668752166416*a(n-31) -125749417451*a(n-32) +60592095948*a(n-33) -5244227851*a(n-34) -1102919206*a(n-35) +264396239*a(n-36) -12021054*a(n-37) -1712600*a(n-38) +222192*a(n-39) -8748*a(n-40) +108*a(n-41) for n>45

%e Some solutions for n=3

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 22 2013

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Last modified August 3 08:07 EDT 2024. Contains 374885 sequences. (Running on oeis4.)