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 A231855 T(n,k)=Number of nXk 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions) 13
 1, 1, 3, 3, 8, 9, 8, 34, 55, 27, 21, 144, 656, 377, 81, 55, 612, 7339, 12404, 2584, 243, 144, 2613, 85288, 360966, 234336, 17711, 729, 377, 11159, 991167, 11149456, 17726611, 4426924, 121393, 2187, 987, 47675, 11529929, 342945563, 1454768048, 870478586 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Table starts ....1......1..........3.............8...............21..................55 ....3......8.........34...........144..............612................2613 ....9.....55........656..........7339............85288..............991167 ...27....377......12404........360966.........11149456...........342945563 ...81...2584.....234336......17726611.......1454768048........118292347982 ..243..17711....4426924.....870478586.....189801034186......40798265169064 ..729.121393...83630516...42745416641...24762957054535...14071005227913420 .2187.832040.1579892344.2099041399895.3230773305296573.4852980371902817445 LINKS R. H. Hardin, Table of n, a(n) for n = 1..161 FORMULA Empirical for column k: k=1: a(n) = 3*a(n-1) k=2: a(n) = 7*a(n-1) -a(n-2) k=3: a(n) = 21*a(n-1) -41*a(n-2) +22*a(n-3) for n>4 k=4: [order 9] for n>10 k=5: [order 21] for n>22 k=6: [order 52] for n>54 Empirical for row n: n=1: a(n) = 3*a(n-1) -a(n-2) for n>3 n=2: [order 8] for n>9 n=3: [order 35] for n>39 EXAMPLE Some solutions for n=3 k=4 ..0..0..0..1....0..0..2..1....0..0..0..0....0..0..0..1....0..0..1..0 ..0..2..2..2....1..2..1..1....1..1..1..1....0..0..2..2....0..2..0..1 ..2..0..0..0....1..1..2..2....1..2..0..0....1..0..0..0....2..2..2..2 CROSSREFS Column 1 is A000244(n-1) Column 2 is A033890(n-1) Row 1 is A001906(n-1) Sequence in context: A248696 A021299 A141678 * A368738 A135477 A182473 Adjacent sequences: A231852 A231853 A231854 * A231856 A231857 A231858 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Nov 14 2013 STATUS approved

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Last modified March 4 05:23 EST 2024. Contains 370522 sequences. (Running on oeis4.)