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 A231908 T(n,k)=Number of nXk 0..2 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions) 10
 1, 1, 3, 3, 17, 9, 8, 137, 74, 27, 21, 948, 1740, 315, 81, 55, 6975, 31167, 22759, 1343, 243, 144, 50323, 614818, 1082472, 297099, 5734, 729, 377, 366170, 11900005, 57946241, 37368831, 3882566, 24495, 2187, 987, 2657785, 232002949, 3045772177 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Table starts ....1......1.........3.............8...............21...................55 ....3.....17.......137...........948.............6975................50323 ....9.....74......1740.........31167...........614818.............11900005 ...27....315.....22759.......1082472.........57946241...........3045772177 ...81...1343....297099......37368831.......5429359691.........773715251151 ..243...5734...3882566....1291573433.....509273459716......196795864115357 ..729..24495..50739125...44640322903...47773200503463....50062652312668838 .2187.104655.663117735.1542901809201.4481443113541663.12735271817562619233 LINKS R. H. Hardin, Table of n, a(n) for n = 1..96 FORMULA Empirical for column k: k=1: a(n) = 3*a(n-1) k=2: a(n) = 6*a(n-1) -8*a(n-2) +2*a(n-3) +3*a(n-4) -a(n-5) for n>6 k=3: [order 17] for n>18 k=4: [order 81] for n>82 Empirical for row n: n=1: a(n) = 3*a(n-1) -a(n-2) for n>3 n=2: a(n) = 9*a(n-1) -5*a(n-2) -66*a(n-3) +78*a(n-4) +4*a(n-5) -16*a(n-6) n=3: [order 37] for n>38 EXAMPLE Some solutions for n=3 k=4 ..0..0..2..1....0..0..0..1....0..2..0..1....0..2..2..1....0..0..0..0 ..1..0..1..1....2..1..0..0....2..2..2..0....2..2..1..2....0..0..1..0 ..0..2..0..0....1..2..2..1....2..0..0..2....2..0..0..1....1..1..0..2 CROSSREFS Column 1 is A000244(n-1) Column 2 is A231779 Row 1 is A001906(n-1) Sequence in context: A127539 A342837 A278627 * A226610 A332840 A279172 Adjacent sequences: A231905 A231906 A231907 * A231909 A231910 A231911 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Nov 15 2013 STATUS approved

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Last modified August 5 02:04 EDT 2024. Contains 374935 sequences. (Running on oeis4.)