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.

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

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

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

Adjacent sequences: A211836 A211837 A211838 * A211840 A211841 A211842

Keyword

nonn

Author

R. H. Hardin, Apr 21 2012

Status

approved