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A216938 Number of side-2 hexagonal 0..n arrays with values nondecreasing E, SW and SE 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Row 2 of A216937.
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Sep 20 2012
STATUS
approved

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Last modified June 13 00:48 EDT 2024. Contains 373362 sequences. (Running on oeis4.)