A229445 - OEIS

%I #4 Sep 23 2013 07:46:03

%S 3,4,5,5,7,8,6,10,13,12,7,14,22,25,17,8,19,37,53,47,23,9,25,60,109,

%T 128,84,30,10,32,93,212,324,293,142,38,11,40,138,387,753,915,625,228,

%U 47,12,49,197,665,1609,2546,2402,1244,350,57,13,59,272,1083,3184,6374,8024

%N T(n,k)=Number of nXk 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing

%C Table starts

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

%C ..5...7...10...14....19....25.....32.....40......49......59......70.......82

%C ..8..13...22...37....60....93....138....197.....272.....365.....478......613

%C .12..25...53..109...212...387....665...1083....1684....2517....3637.....5105

%C .17..47..128..324...753..1609...3184...5890...10281...17075...27176....41696

%C .23..84..293..915..2546..6374..14536..30571...59969..110816..194535...326723

%C .30.142..625.2402..8024.23610..62205.149031..329106..677706.1314145..2419348

%C .38.228.1244.5843.23428.81177.247607.676983.1685570.3873314.8307126.16784531

%H R. H. Hardin, <a href="/A229445/b229445.txt">Table of n, a(n) for n = 1..480</a>

%F Empirical for column k:

%F k=1: a(n) = (1/2)*n^2 + (1/2)*n + 2

%F k=2: a(n) = (1/24)*n^4 + (1/12)*n^3 - (1/24)*n^2 + (23/12)*n + 2

%F k=3: [polynomial of degree 6]

%F k=4: [polynomial of degree 8]

%F k=5: [polynomial of degree 10]

%F k=6: [polynomial of degree 12]

%F k=7: [polynomial of degree 14]

%F Empirical for row n:

%F n=1: a(n) = n + 2

%F n=2: a(n) = (1/2)*n^2 + (1/2)*n + 4

%F n=3: a(n) = (1/3)*n^3 + (8/3)*n + 5

%F n=4: a(n) = (1/4)*n^4 - (1/3)*n^3 + (13/4)*n^2 + (11/6)*n + 7

%F n=5: a(n) = (11/60)*n^5 - (1/2)*n^4 + (15/4)*n^3 - n^2 + (257/30)*n + 6

%F n=6: [polynomial of degree 6]

%F n=7: [polynomial of degree 7]

%e Some solutions for n=4 k=4

%e ..0..2..2..2....0..2..2..2....0..0..2..2....0..0..2..2....0..2..2..2

%e ..1..0..0..2....1..0..0..0....0..0..2..2....1..1..0..0....0..2..2..2

%e ..2..1..1..0....2..1..1..1....1..1..0..0....1..1..1..1....0..2..2..2

%e ..2..1..1..1....2..2..2..2....1..1..1..1....2..2..1..1....1..0..0..2

%Y Column 1 is A022856(n+4)

%Y Row 2 is A145018(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Sep 23 2013