login
Number of 2Xn 0..3 arrays with every repeated value in every row greater than or equal to, and in every column greater than, the previous repeated value.
2

%I #4 Jan 23 2016 10:03:25

%S 16,256,4096,62500,929296,13498276,192321424,2695374889,37241280400,

%T 508180785424,6858511503376,91659848427225,1214228383808400,

%U 15957351268208100,208196756833645584,2698422754887026244

%N Number of 2Xn 0..3 arrays with every repeated value in every row greater than or equal to, and in every column greater than, the previous repeated value.

%C Row 2 of A267974.

%H R. H. Hardin, <a href="/A267976/b267976.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 70*a(n-1) -2030*a(n-2) +30793*a(n-3) -246680*a(n-4) +794920*a(n-5) +1553979*a(n-6) -13039450*a(n-7) -13949950*a(n-8) +88507965*a(n-9) +242460400*a(n-10) +242460400*a(n-11) +88507965*a(n-12) -13949950*a(n-13) -13039450*a(n-14) +1553979*a(n-15) +794920*a(n-16) -246680*a(n-17) +30793*a(n-18) -2030*a(n-19) +70*a(n-20) -a(n-21)

%e Some solutions for n=4

%e ..0..3..3..2....0..3..3..2....0..2..1..0....1..0..3..1....1..0..2..0

%e ..1..2..0..0....1..0..2..0....3..0..1..3....1..3..1..2....3..2..1..1

%Y Cf. A267974.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 23 2016