A250223 - OEIS

%I #9 Nov 12 2018 14:38:26

%S 3,11,27,79,223,651,1907,5639,16967,52131,163291,518687,1659887,

%T 5320123,17004227,54054071,170674327,535082323,1666053035,5154907599,

%U 15861068351,48568847467,148122439315,450214152039,1364634624743,4127055619331

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

%H R. H. Hardin, <a href="/A250223/b250223.txt">Table of n, a(n) for n = 1..104</a>

%F Empirical: a(n) = 15*a(n-1) - 98*a(n-2) + 366*a(n-3) - 861*a(n-4) + 1323*a(n-5) - 1328*a(n-6) + 840*a(n-7) - 304*a(n-8) + 48*a(n-9) for n>12.

%F Empirical g.f.: x*(3 - 34*x + 156*x^2 - 346*x^3 + 241*x^4 + 668*x^5 - 2240*x^6 + 3600*x^7 - 3984*x^8 + 3200*x^9 - 1664*x^10 + 384*x^11) / ((1 - x)^4*(1 - 2*x)^4*(1 - 3*x)). - _Colin Barker_, Nov 12 2018

%e Some solutions for n=6:

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

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

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

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

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

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

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

%Y Column 2 of A250229.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 14 2014