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A223801 T(n,k)=Number of nXk 0..3 arrays with rows and antidiagonals unimodal.

%I A223801 #6 Jul 23 2025 04:32:16
%S A223801 4,16,16,50,256,64,130,2500,4096,256,296,16900,110116,65536,1024,610,
%T A223801 87616,1658703,4816168,1048576,4096,1163,372100,16979881,151310069,
%U A223801 210163664,16777216,16384,2083,1352569,131295500,2844578252,13602542576
%N A223801 T(n,k)=Number of nXk 0..3 arrays with rows and antidiagonals unimodal.
%C A223801 Table starts
%C A223801 .......4............16................50..................130
%C A223801 ......16...........256..............2500................16900
%C A223801 ......64..........4096............110116..............1658703
%C A223801 .....256.........65536...........4816168............151310069
%C A223801 ....1024.......1048576.........210163664..........13602542576
%C A223801 ....4096......16777216........9169032476........1216562667529
%C A223801 ...16384.....268435456......400006582368......108631485025292
%C A223801 ...65536....4294967296....17450517286804.....9695922803812530
%C A223801 ..262144...68719476736...761287955888788...865293308203272685
%C A223801 .1048576.1099511627776.33211580867804324.77218182866179219113
%H A223801 R. H. Hardin, <a href="/A223801/b223801.txt">Table of n, a(n) for n = 1..198</a>
%F A223801 Empirical for column k:
%F A223801 k=1: a(n) = 4*a(n-1)
%F A223801 k=2: a(n) = 16*a(n-1)
%F A223801 k=3: [order 10]
%F A223801 k=4: [order 27]
%F A223801 Empirical: rows n=1..6 are polynomials of degree 6*n for k>0,0,0,0,2,3
%e A223801 Some solutions for n=3 k=4
%e A223801 ..0..0..0..3....0..0..1..1....0..2..3..3....0..2..3..1....0..2..1..1
%e A223801 ..1..2..2..3....0..2..3..3....2..2..2..0....0..0..0..0....2..2..2..3
%e A223801 ..1..1..3..2....0..1..1..2....2..1..0..0....0..0..2..3....2..2..1..0
%Y A223801 Column 1 is A000302
%Y A223801 Column 2 is A001025
%Y A223801 Row 1 is A223659
%Y A223801 Row 2 is A223756
%K A223801 nonn,tabl
%O A223801 1,1
%A A223801 _R. H. Hardin_ Mar 27 2013