cp's OEIS Frontend

A269622 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

%I A269622 #7 Jan 25 2019 08:27:48
%S A269622 51,624,3611,14125,43013,110099,248143,507521,961625,1712983,2900099,
%T A269622 4705013,7361581,11164475,16478903,23751049,33519233,46425791,
%U A269622 63229675,84819773,112228949,146648803,189445151,242174225,306599593,384709799
%N A269622 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.
%H A269622 R. H. Hardin, <a href="/A269622/b269622.txt">Table of n, a(n) for n = 1..210</a>
%F A269622 Empirical: a(n) = n^6 + 6*n^5 + 9*n^4 + 22*n^3 + 9*n^2 + 9*n - 7 for n>2.
%F A269622 Conjectures from _Colin Barker_, Jan 25 2019: (Start)
%F A269622 G.f.: x*(51 + 267*x + 314*x^2 + 167*x^3 - 86*x^4 + 17*x^5 - 14*x^6 + 5*x^7 - x^8) / (1 - x)^7.
%F A269622 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>9.
%F A269622 (End)
%e A269622 Some solutions for n=6:
%e A269622 ..1. .2. .0. .5. .3. .1. .1. .5. .3. .0. .5. .4. .0. .3. .0. .2
%e A269622 ..6. .2. .2. .0. .6. .4. .0. .1. .3. .5. .2. .1. .6. .2. .5. .4
%e A269622 ..3. .3. .0. .5. .3. .5. .1. .4. .3. .5. .4. .0. .5. .1. .5. .4
%e A269622 ..3. .1. .2. .2. .1. .4. .2. .3. .3. .4. .3. .3. .4. .4. .5. .0
%e A269622 ..6. .1. .6. .4. .4. .3. .5. .4. .2. .5. .6. .3. .1. .1. .4. .2
%e A269622 ..4. .3. .0. .3. .3. .0. .5. .4. .1. .5. .3. .1. .4. .2. .4. .5
%Y A269622 Row 6 of A269619.
%K A269622 nonn
%O A269622 1,1
%A A269622 _R. H. Hardin_, Mar 01 2016