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A211839
Number of nonnegative integer arrays of length n+6 with new values 0 upwards introduced in order, no three adjacent elements equal, and containing the value n+1.
1
664, 2621, 9068, 27312, 72840, 175475, 388512, 801674, 1558833, 2881546, 5099561, 8689553, 14323455, 22927854, 35756027, 54474297, 81264494, 118944411, 171108250, 242289158, 338146058, 465677085, 633462042, 851936396, 1133699439
OFFSET
1,1
COMMENTS
Row 5 of A211836.
LINKS
FORMULA
Empirical: a(n) = (1/384)*n^8 + (7/96)*n^7 + (515/576)*n^6 + (499/80)*n^5 + (31603/1152)*n^4 + (7763/96)*n^3 + (47569/288)*n^2 + (8973/40)*n + 159.
Conjectures from Colin Barker, Jul 20 2018: (Start)
G.f.: x*(664 - 3355*x + 9383*x^2 - 15720*x^3 + 16980*x^4 - 11983*x^5 + 5367*x^6 - 1390*x^7 + 159*x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)
EXAMPLE
Some solutions for n=3:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....0....1....1....1....1....1....1....1....1....1....1
..2....2....1....2....0....1....1....2....2....2....2....2....1....2....2....2
..0....0....2....3....2....2....2....0....3....1....3....3....2....1....3....3
..3....3....3....4....3....3....0....3....4....0....3....3....3....2....4....4
..2....3....4....0....3....1....3....4....2....1....4....2....1....3....4....5
..2....0....2....5....4....1....4....5....5....1....4....4....4....3....1....5
..3....1....1....2....0....2....0....1....0....3....5....5....0....4....1....6
..4....4....4....0....0....4....2....6....2....4....6....1....4....3....0....7
CROSSREFS
Cf. A211836.
Sequence in context: A105978 A208180 A317396 * A171395 A069426 A093733
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 21 2012
STATUS
approved