cp's OEIS Frontend

A250271 Number of length n+1 0..2 arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.

%I A250271 #14 Aug 11 2025 17:14:02
%S A250271 3,11,27,79,255,843,2763,8903,28215,88195,272739,836607,2550735,
%T A250271 7742267,23423355,70695991,213005415,640982259,1927141011,5790335855,
%U A250271 17389881855,52209491371,156712360107,470313240999,1411308821655,4234698216803,12705705263043,38120471232223
%N A250271 Number of length n+1 0..2 arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.
%H A250271 R. H. Hardin, <a href="/A250271/b250271.txt">Table of n, a(n) for n = 1..210</a>
%F A250271 Empirical: a(n) = 9*a(n-1) - 31*a(n-2) + 51*a(n-3) - 40*a(n-4) + 12*a(n-5) for n>6.
%F A250271 Conjectures from _Colin Barker_, Nov 12 2018: (Start)
%F A250271 G.f.: x*(3 - 16*x + 21*x^2 + 24*x^3 - 60*x^4 + 24*x^5) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)).
%F A250271 a(n) = 5*3^(n-1) - (2^n-2)*n for n>1. (End)
%e A250271 Some solutions for n=6:
%e A250271 ..0....0....2....0....0....2....2....0....2....2....2....1....2....2....1....0
%e A250271 ..1....1....1....2....0....1....1....1....0....2....1....2....0....2....1....1
%e A250271 ..1....2....1....2....1....2....2....1....0....2....0....2....0....2....1....2
%e A250271 ..2....1....2....0....1....0....1....2....1....0....0....0....0....0....1....2
%e A250271 ..2....2....0....0....1....2....2....0....0....2....0....1....1....2....2....2
%e A250271 ..0....2....2....1....1....0....1....1....1....1....1....2....0....1....2....1
%e A250271 ..2....0....2....2....2....2....2....2....0....2....2....1....2....0....1....0
%Y A250271 Column 2 of A250277.
%K A250271 nonn
%O A250271 1,1
%A A250271 _R. H. Hardin_, Nov 16 2014