A216938 Number of side-2 hexagonal 0..n arrays with values nondecreasing E, SW and SE

10, 53, 200, 606, 1572, 3630, 7656, 15015, 27742, 48763, 82160, 133484, 210120, 321708, 480624, 702525, 1006962, 1418065, 1965304, 2684330, 3617900, 4816890, 6341400, 8261955, 10660806, 13633335, 17289568, 21755800, 27176336, 33715352

Offset

1,1

Comments

Row 2 of A216937.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (1/1260)*n^7 + (1/60)*n^6 + (53/360)*n^5 + (17/24)*n^4 + (719/360)*n^3 + (131/40)*n^2 + (1199/420)*n + 1= (n+5) *(n+4) *(n+3) *(n+2) *(n+1) *(2*n^2+12*n+21)/2520.

Conjectures from Colin Barker, Jul 23 2018: (Start)

G.f.: x*(5 - 6*x + 4*x^2 - x^3)*(2 - 3*x + 6*x^2 - 4*x^3 + x^4) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

Some solutions for n=3:
....0.2......0.1......0.2......0.2......0.1......0.0......0.1......0.1
...2.2.2....1.2.2....1.2.2....1.2.2....0.2.2....0.0.2....0.1.2....0.2.2
....3.3......3.3......3.3......2.3......3.3......1.3......1.2......2.2

Crossrefs

Cf. A216937.

Sequence in context: A200035 A119543 A302302 * A298564 A063899 A006889

Adjacent sequences: A216935 A216936 A216937 * A216939 A216940 A216941

Keyword

nonn

Author

R. H. Hardin, Sep 20 2012

Status

approved