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 A223692 T(n,k)=Petersen graph (8,2) coloring a rectangular array: number of nXk 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph 13
 16, 48, 256, 144, 432, 4096, 432, 2304, 3888, 65536, 1296, 12384, 37008, 34992, 1048576, 3888, 66816, 363600, 595584, 314928, 16777216, 11664, 361440, 3788640, 10817856, 9594000, 2834352, 268435456, 34992, 1958400, 40075632, 223096320 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ............16..........48............144..............432.................1296 ...........256.........432...........2304............12384................66816 ..........4096........3888..........37008...........363600..............3788640 .........65536.......34992.........595584.........10817856............223096320 .......1048576......314928........9594000........324280368..........13402129824 ......16777216.....2834352......154616832.......9762152544.........814399853760 .....268435456....25509168.....2492365968.....294583794768.......49817845241568 ....4294967296...229582512....40180445568....8901308553408.....3059068970173824 ...68719476736..2066242608...647800215696..269168305340592...188252023352797728 .1099511627776.18596183472.10444288589568.8142829402619232.11599193857488796224 LINKS R. H. Hardin, Table of n, a(n) for n = 1..218 FORMULA Empirical for column k: k=1: a(n) = 16*a(n-1) k=2: a(n) = 9*a(n-1) k=3: a(n) = 24*a(n-1) -127*a(n-2) k=4: a(n) = 59*a(n-1) -1103*a(n-2) +7621*a(n-3) -16900*a(n-4) k=5: [order 7] for n>8 k=6: [order 17]) for n>18 k=7: [order 37] for n>39 Empirical for row n: n=1: a(n) = 3*a(n-1) n=2: a(n) = 8*a(n-1) -11*a(n-2) -16*a(n-3) for n>4 n=3: a(n) = [order 10]) for n>12 n=4: a(n) = [order 24] for n>27 n=5: a(n) = [order 56] for n>61 EXAMPLE Some solutions for n=3 k=4 ..2..1..9..1....6..5..4..5....6.14..6.14....4..3..2.10....2..3..4..3 ..2..1..9.11....4..5..6.14...12.14..8.14....2.10..2.10....4..3.11.13 ..9.11..9.15....6..7..6.14....8..0..8..0....8.10..8.10...11.13.11..9 CROSSREFS Column 1 is A001025 Column 2 is 48*9^(n-1) Row 1 is A188825(n+1) Sequence in context: A223395 A202329 A223599 * A165115 A165117 A226966 Adjacent sequences: A223689 A223690 A223691 * A223693 A223694 A223695 KEYWORD nonn,tabl AUTHOR R. H. Hardin Mar 25 2013 STATUS approved

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Last modified December 10 12:10 EST 2023. Contains 367710 sequences. (Running on oeis4.)