cp's OEIS Frontend

A223576 T(n,k)=Number of nXk 0..2 arrays with antidiagonals unimodal.

%I A223576 #8 Jul 23 2025 04:15:01
%S A223576 3,9,9,27,81,27,81,729,729,81,243,6561,16038,6561,243,729,59049,
%T A223576 352836,352836,59049,729,2187,531441,7762392,16230456,7762392,531441,
%U A223576 2187,6561,4782969,170772624,746600976,746600976,170772624,4782969,6561,19683
%N A223576 T(n,k)=Number of nXk 0..2 arrays with antidiagonals unimodal.
%C A223576 Table starts
%C A223576 .....3..........9.............27.................81...................243
%C A223576 .....9.........81............729...............6561.................59049
%C A223576 ....27........729..........16038.............352836...............7762392
%C A223576 ....81.......6561.........352836...........16230456.............746600976
%C A223576 ...243......59049........7762392..........746600976...........64207683936
%C A223576 ...729.....531441......170772624........34343644896.........5521860818496
%C A223576 ..2187....4782969.....3756997728......1579807665216.......474880030390656
%C A223576 ..6561...43046721....82653950016.....72671152599936.....40839682613596416
%C A223576 .19683..387420489..1818386900352...3342873019597056...3512212704769291776
%C A223576 .59049.3486784401.40004511807744.153772158901464576.302050292610159092736
%H A223576 R. H. Hardin, <a href="/A223576/b223576.txt">Table of n, a(n) for n = 1..1000</a>
%F A223576 Let U(z) = (z^4+6*z^3+23*z^2+18*z+24)/24
%F A223576 T(n,k) = U(min(n,k))^(max(n,k)-min(n,k)+1) * product{ U(i)^2 , i=1..(min(n,k)-1) }
%e A223576 Some solutions for n=3 k=4
%e A223576 ..0..1..2..2....0..2..0..1....0..1..2..2....0..0..1..2....0..1..0..2
%e A223576 ..0..1..2..2....1..1..2..0....1..1..0..1....1..2..1..2....0..2..1..0
%e A223576 ..1..2..1..1....1..2..0..1....1..0..2..2....1..0..2..0....0..1..0..0
%Y A223576 Column 1 is A000244
%Y A223576 Column 2 is A001019
%K A223576 nonn,tabl
%O A223576 1,1
%A A223576 _R. H. Hardin_ Mar 22 2013