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 A223599 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, diagonal or antidiagonal neighbor moves along an edge of this graph 13
 16, 48, 256, 144, 256, 4096, 432, 1504, 1376, 65536, 1296, 6736, 16192, 7424, 1048576, 3888, 32768, 122608, 176224, 40160, 16777216, 11664, 156592, 1124064, 2372080, 1931968, 217600, 268435456, 34992, 755200, 9902320, 43725920, 47659632 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ............16........48..........144.............432...............1296 ...........256.......256.........1504............6736..............32768 ..........4096......1376........16192..........122608............1124064 .........65536......7424.......176224.........2372080...........43725920 .......1048576.....40160......1931968........47659632.........1807461152 ......16777216....217600.....21308000.......982848688........77164934624 .....268435456...1180256....236213312.....20631729648......3355919411936 ....4294967296...6405888...2629972704....438231627440....147579242411936 ...68719476736..34782688..29389265856...9379905920496...6534353238114336 .1099511627776.188912640.329426847840.201754894742320.290550417324168160 LINKS R. H. Hardin, Table of n, a(n) for n = 1..161 FORMULA Empirical for column k: k=1: a(n) = 16*a(n-1) k=2: a(n) = 8*a(n-1) -11*a(n-2) -16*a(n-3) k=3: a(n) = 23*a(n-1) -153*a(n-2) +217*a(n-3) +258*a(n-4) -456*a(n-5) -104*a(n-6) +192*a(n-7) k=4: [order 9] k=5: [order 29] k=6: [order 55] Empirical for row n: n=1: a(n) = 3*a(n-1) n=2: a(n) = 6*a(n-1) +3*a(n-2) -42*a(n-3) -8*a(n-4) +48*a(n-5) for n>6 n=3: [order 11] for n>12 n=4: [order 28] for n>29 n=5: [order 74] for n>75 EXAMPLE Some solutions for n=3 k=4 .14..6..5.13...13.15..9.15...12..4.12.10....6..5.13.15....8.14..8.10 ..7..6..5..6...13.15..9..1...12..4.12..4....6..5.13..5....8.14..8.14 ..5..6.14..6....9.15..9.11....5..4.12.14...13..5..6..5....6.14..6.14 CROSSREFS Column 1 is A001025 Column 2 is A223434 Row 1 is A188825(n+1) Sequence in context: A109098 A223395 A202329 * A223692 A165115 A165117 Adjacent sequences: A223596 A223597 A223598 * A223600 A223601 A223602 KEYWORD nonn,tabl AUTHOR R. H. Hardin Mar 23 2013 STATUS approved

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Last modified January 31 01:07 EST 2023. Contains 359947 sequences. (Running on oeis4.)