|
%I #6 Mar 27 2013 08:18:07
%S 3,9,9,22,81,27,46,484,729,81,86,2116,8635,6561,243,148,7396,62365,
%T 151580,59049,729,239,21904,334230,1560013,2703137,531441,2187,367,
%U 57121,1455816,11012718,39387861,48302789,4782969,6561,541,134689,5425943
%N T(n,k)=Number of nXk 0..2 arrays with rows, diagonals and antidiagonals unimodal
%C Table starts
%C .....3..........9............22..............46................86
%C .....9.........81...........484............2116..............7396
%C ....27........729..........8635...........62365............334230
%C ....81.......6561........151580.........1560013..........11012718
%C ...243......59049.......2703137........39387861.........343454446
%C ...729.....531441......48302789......1026135371.......11150023974
%C ..2187....4782969.....862007289.....27088106846......377163884938
%C ..6561...43046721...15379566078....715394830136....12972494260444
%C .19683..387420489..274427327200..18858304684055...446829906314726
%C .59049.3486784401.4896915028511.496722962933967.15355124632228358
%H R. H. Hardin, <a href="/A223789/b223789.txt">Table of n, a(n) for n = 1..126</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1)
%F k=2: a(n) = 9*a(n-1)
%F k=3: [order 15]
%F k=4: [order 80]
%F Empirical: rows n=1..5 are polynomials of order 4*n for k>0,0,1,8,15
%e Some solutions for n=3 k=4
%e ..2..2..2..1....1..2..0..0....1..1..2..2....1..2..1..1....0..0..0..0
%e ..0..2..2..1....0..0..1..0....0..2..2..1....1..1..2..0....0..1..2..0
%e ..2..1..0..0....0..1..0..0....0..2..0..0....2..2..2..2....0..0..1..0
%Y Column 1 is A000244
%Y Column 2 is A001019
%Y Row 1 is A223718
%Y Row 2 is A223719
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Mar 27 2013
| 