cp's OEIS Frontend

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).

%I A231855 #6 Jun 02 2025 08:48:28
%S A231855 1,1,3,3,8,9,8,34,55,27,21,144,656,377,81,55,612,7339,12404,2584,243,
%T A231855 144,2613,85288,360966,234336,17711,729,377,11159,991167,11149456,
%U A231855 17726611,4426924,121393,2187,987,47675,11529929,342945563,1454768048,870478586
%N 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).
%C A231855 Table starts
%C A231855 ....1......1..........3.............8...............21..................55
%C A231855 ....3......8.........34...........144..............612................2613
%C A231855 ....9.....55........656..........7339............85288..............991167
%C A231855 ...27....377......12404........360966.........11149456...........342945563
%C A231855 ...81...2584.....234336......17726611.......1454768048........118292347982
%C A231855 ..243..17711....4426924.....870478586.....189801034186......40798265169064
%C A231855 ..729.121393...83630516...42745416641...24762957054535...14071005227913420
%C A231855 .2187.832040.1579892344.2099041399895.3230773305296573.4852980371902817445
%H A231855 R. H. Hardin, <a href="/A231855/b231855.txt">Table of n, a(n) for n = 1..161</a>
%F A231855 Empirical for column k:
%F A231855 k=1: a(n) = 3*a(n-1)
%F A231855 k=2: a(n) = 7*a(n-1) -a(n-2)
%F A231855 k=3: a(n) = 21*a(n-1) -41*a(n-2) +22*a(n-3) for n>4
%F A231855 k=4: [order 9] for n>10
%F A231855 k=5: [order 21] for n>22
%F A231855 k=6: [order 52] for n>54
%F A231855 Empirical for row n:
%F A231855 n=1: a(n) = 3*a(n-1) -a(n-2) for n>3
%F A231855 n=2: [order 8] for n>9
%F A231855 n=3: [order 35] for n>39
%e A231855 Some solutions for n=3 k=4
%e A231855 ..0..0..0..1....0..0..2..1....0..0..0..0....0..0..0..1....0..0..1..0
%e A231855 ..0..2..2..2....1..2..1..1....1..1..1..1....0..0..2..2....0..2..0..1
%e A231855 ..2..0..0..0....1..1..2..2....1..2..0..0....1..0..0..0....2..2..2..2
%Y A231855 Column 1 is A000244(n-1)
%Y A231855 Column 2 is A033890(n-1)
%Y A231855 Row 1 is A001906(n-1)
%K A231855 nonn,tabl
%O A231855 1,3
%A A231855 _R. H. Hardin_, Nov 14 2013