A219502 - OEIS

%I #4 Nov 20 2012 21:20:31

%S 2,2,2,3,3,3,4,5,5,4,5,7,11,7,5,6,9,18,18,9,6,7,11,26,35,26,11,7,8,13,

%T 35,58,58,35,13,8,9,15,45,88,107,88,45,15,9,10,17,56,126,179,179,126,

%U 56,17,10,11,19,68,173,281,325,281,173,68,19,11,12,21,81,230,421,550,550,421

%N T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 nXk array

%C Table starts

%C ..2..2...3...4....5....6.....7.....8.....9....10....11....12....13....14....15

%C ..2..3...5...7....9...11....13....15....17....19....21....23....25....27....29

%C ..3..5..11..18...26...35....45....56....68....81....95...110...126...143...161

%C ..4..7..18..35...58...88...126...173...230...298...378...471...578...700...838

%C ..5..9..26..58..107..179...281...421...608...852..1164..1556..2041..2633..3347

%C ..6.11..35..88..179..325...550...885..1369..2050..2986..4246..5911..8075.10846

%C ..7.13..45.126..281..550...995..1703..2793..4424..6804.10200.14949.21470.30277

%C ..8.15..56.173..421..885..1703..3083..5328..8869.14306.22458.34423.51649.76017

%C ..9.17..68.230..608.1369..2793..5328..9663.16831.28346.46382.74003

%C .10.19..81.298..852.2050..4424..8869.16831.30581.53601.91116

%C .11.21..95.378.1164.2986..6804.14306.28346.53601.97541

%C .12.23.110.471.1556.4246.10200.22458.46382.91116

%H R. H. Hardin, <a href="/A219502/b219502.txt">Table of n, a(n) for n = 1..239</a>

%F Empirical for column k:

%F k=1: a(n) = n for n>1

%F k=2: a(n) = 2*n - 1 for n>1

%F k=3: a(n) = (1/2)*n^2 + (7/2)*n - 4 for n>1

%F k=4: a(n) = (1/6)*n^3 + n^2 + (23/6)*n - 7 for n>2

%F k=5: a(n) = (1/24)*n^4 + (1/4)*n^3 + (35/24)*n^2 + (21/4)*n - 13 for n>2

%F k=6: a(n) = (1/120)*n^5 + (1/24)*n^4 + (13/24)*n^3 + (59/24)*n^2 + (59/20)*n - 17 for n>3

%F k=7: a(n) = (1/720)*n^6 + (1/240)*n^5 + (23/144)*n^4 + (13/16)*n^3 + (331/180)*n^2 + (311/60)*n - 27 for n>3

%e Some solutions for n=3 k=4

%e ..0..0..0..0....0..0..0..0....0..0..0..0....1..0..0..0....1..0..0..0

%e ..0..0..0..0....0..0..0..0....1..0..0..0....1..1..0..0....1..0..0..0

%e ..1..0..0..0....1..1..1..0....1..1..1..0....1..1..1..0....1..0..0..0

%Y Column 1 is A000027

%Y Column 2 is A004273

%Y Column 3 is A056000(n-1) for n>1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Nov 20 2012