A265992 - OEIS

%I #7 Jan 09 2019 09:12:28

%S 1,1,2,2,4,6,7,11,15,26,48,82,135,227,375,634,1088,1850,3135,5315,

%T 8983,15218,25832,43818,74319,126027,213615,362162,614120,1041346,

%U 1765847,2994267,5076959,8608474,14596640,24750370,41967671,71161491,120662599

%N Number of 2 X n integer arrays with each element equal to the number of horizontal and antidiagonal neighbors not equal to itself.

%H R. H. Hardin, <a href="/A265992/b265992.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-3) + a(n-4) + 2*a(n-5) + 2*a(n-6) + 3*a(n-7) + 2*a(n-8) - 4*a(n-9) - 4*a(n-10) - 4*a(n-11) for n>14.

%F Empirical g.f.: x*(1 + x + 2*x^2 - x^3 - 3*x^5 - 5*x^6 - 12*x^7 - 20*x^8 - 17*x^9 - 14*x^10 + 4*x^13) / ((1 - x)*(1 + x)*(1 + x + x^2)*(1 - x - 2*x^3)*(1 + x^2 + 2*x^4)). - _Colin Barker_, Jan 09 2019

%e Some solutions for n=6:

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

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

%Y Row 2 of A265991.

%K nonn

%O 1,3

%A _R. H. Hardin_, Dec 19 2015