A211852 - OEIS

%I #7 Jul 20 2018 08:11:50

%S 588,2013,5486,12713,26163,49210,86275,142968,226230,344475,507732,

%T 727787,1018325,1395072,1875937,2481154,3233424,4158057,5283114,

%U 6639549,8261351,10185686,12453039,15107356,18196186,21770823,25886448,30602271

%N Number of nonnegative integer arrays of length 2n+7 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.

%C Row 6 of A211849.

%H R. H. Hardin, <a href="/A211852/b211852.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (71/60)*n^5 + (337/24)*n^4 + 67*n^3 + (3947/24)*n^2 + (12919/60)*n + 126.

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

%F G.f.: x*(588 - 1515*x + 2228*x^2 - 1768*x^3 + 735*x^4 - 126*x^5) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

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

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

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

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

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

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

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

%e ..3....4....3....3....3....2....3....3....3....1....2....3....4....3....3....4

%e ..4....4....3....4....4....2....3....2....4....2....3....3....3....1....3....4

%e ..3....3....3....4....3....2....4....2....4....2....3....3....3....1....2....3

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

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

%Y Cf. A211849.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 22 2012