A250554 - OEIS

%I #10 Nov 15 2018 03:22:26

%S 2,8,14,32,62,128,254,512,1022,2048,4094,8192,16382,32768,65534,

%T 131072,262142,524288,1048574,2097152,4194302,8388608,16777214,

%U 33554432,67108862,134217728,268435454,536870912,1073741822,2147483648,4294967294

%N Number of length n+2 0..1 arrays with the sum of second differences multiplied by some arrangement of +-1 equal to zero.

%H R. H. Hardin, <a href="/A250554/b250554.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3).

%F Empirical: a(n) = 2^(n+1) for even n, 2^(n+1)-2 for odd n.

%F Empirical g.f.: 2*x*(1 + 2*x - 2*x^2) / ((1 - x)*(1 + x)*(1 - 2*x)). - _Colin Barker_, Nov 14 2018

%e Some solutions for n=6:

%e ..1....1....0....0....0....0....1....0....1....1....0....1....0....1....0....0

%e ..0....1....1....1....0....0....1....1....0....0....1....1....0....1....1....0

%e ..0....1....1....0....1....1....0....1....1....0....1....1....1....0....0....1

%e ..1....1....0....0....0....0....1....1....0....0....0....1....1....0....0....0

%e ..1....0....1....0....0....1....1....1....0....1....0....0....1....0....1....1

%e ..1....1....0....1....1....0....1....1....1....1....0....0....1....1....0....1

%e ..0....1....0....0....1....0....0....1....0....1....0....0....0....0....0....1

%e ..1....1....1....1....1....0....0....0....1....0....1....0....0....0....1....1

%Y Column 1 of A250561.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 25 2014