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

%I A216937 #6 Jul 22 2025 23:36:27
%S A216937 2,3,10,4,53,52,5,200,1211,260,6,606,17336,27768,1256,7,1572,175869,
%T A216937 1664244,618013,5908,8,3630,1374208,64697626,161114424,13312100,27224,
%U A216937 9,7656,8737047,1783839948,25604764159,15316983096,278398992,123432,10
%N A216937 T(n,k)=Number of side-n hexagonal 0..k arrays with values nondecreasing E, SW and SE.
%C A216937 Table starts
%C A216937 ........2...............3....................4........................5
%C A216937 .......10..............53..................200......................606
%C A216937 .......52............1211................17336...................175869
%C A216937 ......260...........27768..............1664244.................64697626
%C A216937 .....1256..........618013............161114424..............25604764159
%C A216937 .....5908........13312100..........15316983096...........10284525151080
%C A216937 ....27224.......278398992........1419691311304.........4096557367365808
%C A216937 ...123432......5675814840......128192490487336......1603120459023088062
%C A216937 ...552400....113227696037....11293174782625768....614279244262328965406
%C A216937 ..2446004...2217264763644...972723674586291992.230325185716748014038168
%C A216937 .10735352..42732777814040.82102763053800998896
%C A216937 .46766200.812306057415128
%H A216937 R. H. Hardin, <a href="/A216937/b216937.txt">Table of n, a(n) for n = 1..98</a>
%F A216937 Empirical for rows:
%F A216937 Row 1 is a polynomial of degree 1
%F A216937 Row 2 is a polynomial of degree 7
%F A216937 Row 3 is a polynomial of degree 19
%e A216937 Some solutions for n=3 k=4
%e A216937 ......0.0.1..........0.0.1..........0.0.0..........0.0.0..........0.0.0
%e A216937 .....0.0.2.4........0.1.3.3........0.0.0.0........0.0.0.1........0.0.2.4
%e A216937 ....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 A216937 .....4.4.4.4........3.4.4.4........1.1.1.3........2.3.3.4........4.4.4.4
%e A216937 ......4.4.4..........4.4.4..........3.3.4..........3.4.4..........4.4.4
%Y A216937 Column 1 is 2*A003583(n-1)
%K A216937 nonn,tabl
%O A216937 1,1
%A A216937 _R. H. Hardin_ Sep 20 2012