A248432 - OEIS

%I #7 Nov 08 2018 08:53:28

%S 80,140,252,462,884,1684,3200,6216,11944,22810,44396,85402,163204,

%T 317716,611248,1168198,2274196,4375320,8362052,16278784,31318664,

%U 59855842,116523764,224179214,428448488,834077068,1604674164,3066832822

%N Number of length n+2 0..7 arrays with every three consecutive terms having the sum of some two elements equal to twice the third.

%H R. H. Hardin, <a href="/A248432/b248432.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 10*a(n-3) - 10*a(n-4) - 22*a(n-6) + 22*a(n-7) + 12*a(n-9) - 12*a(n-10) - a(n-12) + a(n-13).

%F Empirical g.f.: 2*x*(40 + 30*x + 56*x^2 - 295*x^3 - 89*x^4 - 160*x^5 + 588*x^6 + 58*x^7 + 96*x^8 - 317*x^9 - 5*x^10 - 9*x^11 + 27*x^12) / ((1 - x)*(1 - 10*x^3 + 22*x^6 - 12*x^9 + x^12)). -  _Colin Barker_, Nov 08 2018

%e Some solutions for n=6:

%e ..6....6....0....4....2....3....4....6....4....3....2....4....5....2....3....4

%e ..4....2....3....2....3....1....6....4....2....5....3....2....3....4....5....5

%e ..5....4....6....0....4....2....5....5....3....4....1....6....7....3....7....3

%e ..3....0....0....4....5....0....4....3....1....6....5....4....5....5....6....7

%e ..7....2....3....2....3....1....3....1....2....2....3....5....3....4....5....5

%e ..5....4....6....3....7....2....2....2....0....4....7....3....4....3....7....6

%e ..3....6....0....1....5....0....4....0....1....3....5....1....5....5....3....4

%e ..1....5....3....5....6....1....3....1....2....2....3....5....6....4....5....2

%Y Column 7 of A248433.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 06 2014