A216937 - OEIS

A216937

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

2, 3, 10, 4, 53, 52, 5, 200, 1211, 260, 6, 606, 17336, 27768, 1256, 7, 1572, 175869, 1664244, 618013, 5908, 8, 3630, 1374208, 64697626, 161114424, 13312100, 27224, 9, 7656, 8737047, 1783839948, 25604764159, 15316983096, 278398992, 123432, 10

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OFFSET

1,1

COMMENTS

Table starts

........2...............3....................4........................5

.......10..............53..................200......................606

.......52............1211................17336...................175869

......260...........27768..............1664244.................64697626

.....1256..........618013............161114424..............25604764159

.....5908........13312100..........15316983096...........10284525151080

....27224.......278398992........1419691311304.........4096557367365808

...123432......5675814840......128192490487336......1603120459023088062

...552400....113227696037....11293174782625768....614279244262328965406

..2446004...2217264763644...972723674586291992.230325185716748014038168

.10735352..42732777814040.82102763053800998896

.46766200.812306057415128

Row n is the Ehrhart polynomial of degree A003215(n-1) for the polytope with variables x(i) indexed by the side-n hexagonal array, with faces corresponding to the constraints 0 <= x(i) <= 1 and x(i) <= x(j) if j is the E, SW or SE neighbor of i. - Robert Israel, May 20 2026

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..98

Wikipedia, Ehrhart polynomial

FORMULA

Empirical for rows:

Row 1 is a polynomial of degree 1

Row 2 is a polynomial of degree 7

Row 3 is a polynomial of degree 19

EXAMPLE

Some solutions for n=3 k=4

......0.0.1..........0.0.1..........0.0.0..........0.0.0..........0.0.0

.....0.0.2.4........0.1.3.3........0.0.0.0........0.0.0.1........0.0.2.4