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A278807 T(n,k)=Number of nXk 0..2 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order.

%I A278807 #4 Nov 28 2016 13:36:46
%S A278807 3,6,6,10,22,10,15,63,63,15,21,154,322,154,21,28,336,1439,1439,336,28,
%T A278807 36,672,5767,12958,5767,672,36,45,1254,20972,110455,110455,20972,1254,
%U A278807 45,55,2211,69834,870473,2179956,870473,69834,2211,55,66,3718,214774,6275546
%N A278807 T(n,k)=Number of nXk 0..2 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order.
%C A278807 Table starts
%C A278807 ..3....6......10.........15............21...............28.................36
%C A278807 ..6...22......63........154...........336..............672...............1254
%C A278807 .10...63.....322.......1439..........5767............20972..............69834
%C A278807 .15..154....1439......12958........110455...........870473............6275546
%C A278807 .21..336....5767.....110455.......2179956.........41299256..........725674326
%C A278807 .28..672...20972.....870473......41299256.......1976588468........89730161098
%C A278807 .36.1254...69834....6275546.....725674326......89730161098.....10811999412826
%C A278807 .45.2211..214774...41370842...11698232451....3776527762052...1224101415304069
%C A278807 .55.3718..615120..250517485..172994405326..146582077597322.128795068372302728
%C A278807 .66.6006.1653047.1402100369.2356249442222.5255148833158068
%H A278807 R. H. Hardin, <a href="/A278807/b278807.txt">Table of n, a(n) for n = 1..127</a>
%F A278807 Empirical for column k:
%F A278807 k=1: a(n) = (1/2)*n^2 + (3/2)*n + 1
%F A278807 k=2: [polynomial of degree 6]
%F A278807 k=3: [polynomial of degree 16]
%F A278807 k=4: [polynomial of degree 44]
%e A278807 Some solutions for n=4 k=4
%e A278807 ..1..0..0..0. .1..0..0..0. .1..1..1..0. .1..1..0..0. .1..1..0..0
%e A278807 ..1..1..1..0. .1..1..1..0. .2..0..0..2. .2..1..2..2. .2..1..2..2
%e A278807 ..1..2..1..0. .1..2..0..1. .2..1..0..0. .2..2..1..1. .2..2..1..0
%e A278807 ..2..0..1..2. .1..2..0..1. .2..1..0..2. .2..2..2..2. .2..2..1..1
%Y A278807 Diagonal is A229770.
%Y A278807 Column 1 is A000217(n+1).
%Y A278807 Column 2 is A257200(n+1).
%K A278807 nonn,tabl
%O A278807 1,1
%A A278807 _R. H. Hardin_, Nov 28 2016