cp's OEIS Frontend

A269623 Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

%I A269623 #11 Apr 06 2025 11:30:49
%S A269623 92,1740,13544,66925,246798,742487,1923796,4447329,9398090,18471403,
%T A269623 34200192,60232661,101665414,165437055,260787308,399786697,597941826,
%U A269623 874881299,1255127320,1768958013,2453365502,3353114791,4521908484
%N A269623 Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.
%H A269623 R. H. Hardin, <a href="/A269623/b269623.txt">Table of n, a(n) for n = 1..210</a>
%F A269623 Empirical: a(n) = n^7 + 7*n^6 + 11*n^5 + 35*n^4 + 18*n^3 + 36*n^2 - 19*n - 7 for n>2.
%F A269623 Conjectures from _Colin Barker_, Jan 25 2019: (Start)
%F A269623 G.f.: x*(92 + 1004*x + 2200*x^2 + 2141*x^3 - 370*x^4 + 187*x^5 - 340*x^6 + 179*x^7 - 62*x^8 + 9*x^9) / (1 - x)^8.
%F A269623 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>10. (End)
%e A269623 Some solutions for n=4:
%e A269623 ..3. .3. .3. .3. .0. .4. .2. .1. .2. .0. .1. .1. .0. .3. .1. .2
%e A269623 ..1. .4. .2. .3. .0. .0. .4. .0. .4. .1. .1. .0. .3. .3. .2. .2
%e A269623 ..0. .3. .3. .2. .1. .2. .2. .2. .4. .4. .3. .3. .4. .4. .2. .0
%e A269623 ..0. .0. .4. .3. .0. .2. .0. .4. .3. .1. .1. .3. .0. .3. .2. .3
%e A269623 ..4. .3. .0. .0. .2. .3. .3. .2. .2. .0. .2. .3. .1. .4. .3. .1
%e A269623 ..2. .4. .4. .4. .2. .4. .1. .0. .1. .1. .3. .0. .1. .2. .1. .3
%e A269623 ..4. .3. .3. .0. .1. .3. .3. .4. .2. .0. .4. .2. .1. .2. .0. .4
%Y A269623 Row 7 of A269619.
%K A269623 nonn
%O A269623 1,1
%A A269623 _R. H. Hardin_, Mar 01 2016