cp's OEIS Frontend

A221572 Number of 0..7 arrays of length n with each element differing from at least one neighbor by something other than 1.

%I A221572 #8 Jun 02 2025 08:21:51
%S A221572 0,50,314,2500,19014,145800,1116400,8550512,65485386,501533796,
%T A221572 3841097940,29417832750,225302467392,1725524876860,13215284016064,
%U A221572 101211946587176,775152325067630,5936662096954472,45467136862793520
%N A221572 Number of 0..7 arrays of length n with each element differing from at least one neighbor by something other than 1.
%C A221572 Column 7 of A221573
%H A221572 R. H. Hardin, <a href="/A221572/b221572.txt">Table of n, a(n) for n = 1..210</a>
%F A221572 Empirical: a(n) = 7*a(n-1) +4*a(n-2) +5*a(n-3) +20*a(n-4) +20*a(n-5) +23*a(n-6) -6*a(n-7) +3*a(n-8).
%F A221572 Empirical g.f.: -2*x^2*(25-18*x+51*x^2+4*x^3+66*x^4-18*x^5+6*x^6) / ( -1+7*x+4*x^2+5*x^3+20*x^4+20*x^5+23*x^6-6*x^7+3*x^8 ). - _R. J. Mathar_, Jun 06 2013
%e A221572 Some solutions for n=6
%e A221572 ..6....5....1....2....1....3....6....4....4....2....7....0....1....2....2....6
%e A221572 ..4....2....6....7....6....6....0....2....0....7....4....4....6....6....4....2
%e A221572 ..6....4....7....0....0....1....2....2....7....0....2....1....3....2....1....4
%e A221572 ..2....5....4....3....0....4....0....6....4....0....7....1....2....3....6....0
%e A221572 ..6....7....3....3....0....7....7....1....0....1....5....6....5....0....6....1
%e A221572 ..1....7....1....0....5....0....4....1....0....1....3....0....3....0....0....4
%K A221572 nonn
%O A221572 1,2
%A A221572 _R. H. Hardin_ Jan 20 2013