login
Number of length-5 0..n arrays with every repeated value unequal to the previous repeated value plus one mod n+1.
1

%I #8 Jan 29 2019 05:49:46

%S 24,222,984,3060,7680,16674,32592,58824,99720,160710,248424,370812,

%T 537264,758730,1047840,1419024,1888632,2475054,3198840,4082820,

%U 5152224,6434802,7960944,9763800,11879400,14346774,17208072,20508684,24297360

%N Number of length-5 0..n arrays with every repeated value unequal to the previous repeated value plus one mod n+1.

%H R. H. Hardin, <a href="/A269777/b269777.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^5 + 5*n^4 + 10*n^3 + 7*n^2 + n.

%F Conjectures from _Colin Barker_, Jan 29 2019: (Start)

%F G.f.: 6*x*(4 + 13*x + 2*x^2 + x^3) / (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 ..1. .1. .0. .3. .1. .0. .1. .0. .1. .3. .0. .0. .0. .0. .1. .0

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

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

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

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

%Y Row 5 of A269776.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 04 2016