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A216937 T(n,k)=Number of side-n hexagonal 0..k arrays with values nondecreasing E, SW and SE 13

%I #4 Sep 20 2012 15:32:24

%S 2,3,10,4,53,52,5,200,1211,260,6,606,17336,27768,1256,7,1572,175869,

%T 1664244,618013,5908,8,3630,1374208,64697626,161114424,13312100,27224,

%U 9,7656,8737047,1783839948,25604764159,15316983096,278398992,123432,10

%N T(n,k)=Number of side-n hexagonal 0..k arrays with values nondecreasing E, SW and SE

%C Table starts

%C ........2...............3....................4........................5

%C .......10..............53..................200......................606

%C .......52............1211................17336...................175869

%C ......260...........27768..............1664244.................64697626

%C .....1256..........618013............161114424..............25604764159

%C .....5908........13312100..........15316983096...........10284525151080

%C ....27224.......278398992........1419691311304.........4096557367365808

%C ...123432......5675814840......128192490487336......1603120459023088062

%C ...552400....113227696037....11293174782625768....614279244262328965406

%C ..2446004...2217264763644...972723674586291992.230325185716748014038168

%C .10735352..42732777814040.82102763053800998896

%C .46766200.812306057415128

%H R. H. Hardin, <a href="/A216937/b216937.txt">Table of n, a(n) for n = 1..98</a>

%F Empirical for rows:

%F Row 1 is a polynomial of degree 1

%F Row 2 is a polynomial of degree 7

%F Row 3 is a polynomial of degree 19

%e Some solutions for n=3 k=4

%e ......0.0.1..........0.0.1..........0.0.0..........0.0.0..........0.0.0

%e .....0.0.2.4........0.1.3.3........0.0.0.0........0.0.0.1........0.0.2.4

%e ....3.3.3.4.4......1.2.4.4.4......0.0.1.1.1......0.1.1.2.3......0.4.4.4.4

%e .....4.4.4.4........3.4.4.4........1.1.1.3........2.3.3.4........4.4.4.4

%e ......4.4.4..........4.4.4..........3.3.4..........3.4.4..........4.4.4

%Y Column 1 is 2*A003583(n-1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Sep 20 2012

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