A251107 - OEIS

%I #10 Feb 04 2019 03:00:02

%S 147,810,3616,15281,67518,304870,1369052,6118942,27356256,122402144,

%T 547700666,2450461705,10963429165,49051483677,219461893981,

%U 981894966609,4393096675995,19655164658898,87939229945039,393449138915943

%N Number of (n+1) X (2+1) 0..2 arrays with no 2 X 2 subblock having the maximum of its diagonal elements greater than the absolute difference of its antidiagonal elements

%C Column 2 of A251113.

%H R. H. Hardin, <a href="/A251107/b251107.txt">Table of n, a(n) for n = 1..210</a>

%H Robert Israel, <a href="/A251107/a251107.pdf">Maple-assisted proof of empirical recurrence</a>

%F Empirical: a(n) = 11*a(n-1) - 53*a(n-2) + 169*a(n-3) - 400*a(n-4) + 717*a(n-5) - 999*a(n-6) + 1063*a(n-7) - 860*a(n-8) + 543*a(n-9) - 268*a(n-10) + 115*a(n-11) - 40*a(n-12) + 9*a(n-13) - a(n-14).

%F Empirical formula verified: see link. - _Robert Israel_, Feb 03 2019

%e Some solutions for n=4:

%e   0 0 2   1 2 2   0 2 2   1 0 1   0 0 1   0 0 0   0 0 2

%e   0 0 2   0 0 2   1 0 2   1 0 1   0 0 1   2 2 2   0 0 2

%e   0 0 0   1 0 2   1 0 1   1 1 0   1 0 0   0 0 0   0 0 0

%e   2 0 0   1 0 0   2 0 0   0 1 1   1 0 0   2 2 2   1 0 0

%e   2 2 2   2 2 2   2 2 1   0 0 0   2 1 0   0 0 0   2 1 0

%p f:= proc(i,j)

%p   local Li, Lj;

%p   Li:= convert(i+27,base,3)[1..3];

%p   Lj:= convert(j+27,base,3)[1..3];

%p   if max(Li[1],Lj[2])<=abs(Li[2]-Lj[1])

%p     and max(Li[2],Lj[3])<=abs(Li[3]-Lj[2])

%p     then 1 else 0

%p   fi

%p end proc:

%p T:= Matrix(27,27,f):

%p u:= Vector(27,1):

%p Tu[0]:= u:

%p for n from 1 to 30 do Tu[n]:= T . Tu[n-1] od:

%p seq(u^%T . Tu[n], n=1..30); # _Robert Israel_, Feb 03 2019

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 30 2014