A211839 - OEIS

%I #9 May 25 2021 05:12:01

%S 664,2621,9068,27312,72840,175475,388512,801674,1558833,2881546,

%T 5099561,8689553,14323455,22927854,35756027,54474297,81264494,

%U 118944411,171108250,242289158,338146058,465677085,633462042,851936396,1133699439

%N 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.

%C Row 5 of A211836.

%H R. H. Hardin, <a href="/A211839/b211839.txt">Table of n, a(n) for n = 1..210</a>

%F 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.

%F Conjectures from _Colin Barker_, Jul 20 2018: (Start)

%F 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.

%F 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.

%F (End)

%e Some solutions for n=3:

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..1....1....1....1....1....0....1....1....1....1....1....1....1....1....1....1

%e ..2....2....1....2....0....1....1....2....2....2....2....2....1....2....2....2

%e ..0....0....2....3....2....2....2....0....3....1....3....3....2....1....3....3

%e ..3....3....3....4....3....3....0....3....4....0....3....3....3....2....4....4

%e ..2....3....4....0....3....1....3....4....2....1....4....2....1....3....4....5

%e ..2....0....2....5....4....1....4....5....5....1....4....4....4....3....1....5

%e ..3....1....1....2....0....2....0....1....0....3....5....5....0....4....1....6

%e ..4....4....4....0....0....4....2....6....2....4....6....1....4....3....0....7

%Y Cf. A211836.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 21 2012