A265929 - OEIS

A265929

Number of 1 X n 0..4 arrays with the absolute differences of each element with its with horizontal and antidiagonal neighbors unique.

%I #9 Mar 21 2018 06:45:40

%S 5,25,92,340,1252,4616,17012,62696,231044,851496,3138100,11564952,

%T 42620580,157071768,578865076,2133318088,7862009732,28974227016,

%U 106780086132,393521606584,1450263256356,5344722135352,19697152196980

%N Number of 1 X n 0..4 arrays with the absolute differences of each element with its with horizontal and antidiagonal neighbors unique.

%C Row 1 of A265928.

%H R. H. Hardin, <a href="/A265929/b265929.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2) + 10*a(n-3) + 27*a(n-4) - 13*a(n-5) + 28*a(n-6) - 20*a(n-7) - 96*a(n-8) for n>9.

%F Empirical g.f.: x*(1 + x)*(5 + 5*x + 22*x^2 + 42*x^3 - 11*x^4 + 21*x^5 - 52*x^6 - 160*x^7) / (1 - 3*x + 2*x^2 - 10*x^3 - 27*x^4 + 13*x^5 - 28*x^6 + 20*x^7 + 96*x^8). - _Colin Barker_, Mar 21 2018

%e Some solutions for n=4:

%e ..1..3..0..1....0..3..3..1....2..1..3..0....0..1..4..0....1..2..2..0

%Y Cf. A265928.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 18 2015