A248996 - OEIS

%I #7 Nov 09 2018 08:10:21

%S 820,2668,8680,28240,91888,299044,973204,3167500,10309372,33554728,

%T 109215076,355477276,1157029012,3765974644,12257760052,39897482020,

%U 129861371368,422682950584,1375781835724,4478003930896,14575364597464

%N Number of length n+4 0..3 arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

%H R. H. Hardin, <a href="/A248996/b248996.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 2*a(n-2) - a(n-3) - 9*a(n-4) + 16*a(n-5) - 48*a(n-6) - 21*a(n-7) + 8*a(n-8) + 3*a(n-9).

%F Empirical g.f.: 4*x*(205 + 52*x - 241*x^2 - 579*x^3 - 36*x^4 - 3382*x^5 - 1168*x^6 + 563*x^7 + 192*x^8) / (1 - 3*x - 2*x^2 + x^3 + 9*x^4 - 16*x^5 + 48*x^6 + 21*x^7 - 8*x^8 - 3*x^9). - _Colin Barker_, Nov 09 2018

%e Some solutions for n=5:

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

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

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

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

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

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

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

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

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

%Y Column 3 of A249001.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 18 2014