cp's OEIS Frontend

A268947 Number of length-6 0..n arrays with no repeated value unequal to the previous repeated value plus one mod n+1.

%I A268947 #8 Jan 17 2019 05:26:07
%S A268947 22,396,2780,11950,38322,101192,232696,482490,923150,1656292,2819412,
%T A268947 4593446,7211050,10965600,16220912,23421682,33104646,45910460,
%U A268947 62596300,84049182,111300002,145538296,188127720,240622250,304783102,382596372
%N A268947 Number of length-6 0..n arrays with no repeated value unequal to the previous repeated value plus one mod n+1.
%H A268947 R. H. Hardin, <a href="/A268947/b268947.txt">Table of n, a(n) for n = 1..210</a>
%F A268947 Empirical: a(n) = n^6 + 6*n^5 + 5*n^4 + 6*n^3 + 3*n^2 - n + 2.
%F A268947 Conjectures from _Colin Barker_, Jan 17 2019: (Start)
%F A268947 G.f.: 2*x*(11 + 121*x + 235*x^2 + 18*x^3 - 19*x^4 - 7*x^5 + x^6) / (1 - x)^7.
%F A268947 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A268947 (End)
%e A268947 Some solutions for n=6:
%e A268947 ..6. .4. .5. .3. .1. .6. .2. .2. .0. .1. .1. .4. .5. .0. .6. .1
%e A268947 ..4. .3. .2. .3. .6. .1. .6. .2. .2. .5. .3. .6. .6. .5. .2. .4
%e A268947 ..5. .3. .4. .5. .5. .1. .6. .3. .2. .4. .0. .2. .2. .3. .6. .6
%e A268947 ..3. .0. .3. .0. .0. .2. .0. .2. .0. .6. .0. .6. .5. .5. .3. .0
%e A268947 ..1. .3. .4. .4. .5. .0. .2. .6. .1. .0. .2. .5. .1. .4. .6. .4
%e A268947 ..5. .4. .3. .3. .5. .5. .5. .0. .5. .1. .6. .2. .4. .2. .5. .1
%Y A268947 Row 6 of A268944.
%K A268947 nonn
%O A268947 1,1
%A A268947 _R. H. Hardin_, Feb 16 2016