login
Number of length n arrays of permutations of 0..n-1 with each element moved by -6 to 6 places and with no two consecutive increases or two consecutive decreases.
1

%I #4 Oct 23 2015 11:21:30

%S 1,2,4,10,32,122,544,2287,7688,25662,79456,256482,809784,2690604,

%T 8874432,30009480,98599568,332395712,1084222064,3637730112,

%U 11844968640,39726351272,129526799072,434837072968,1418856843552,4764806022144

%N Number of length n arrays of permutations of 0..n-1 with each element moved by -6 to 6 places and with no two consecutive increases or two consecutive decreases.

%C Column 6 of A263666.

%H R. H. Hardin, <a href="/A263664/b263664.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-2) +26*a(n-4) +166*a(n-6) +1096*a(n-8) +5220*a(n-10) +2608*a(n-12) -32104*a(n-14) -26760*a(n-16) +18920*a(n-18) -246704*a(n-20) -102880*a(n-22) +272224*a(n-24) -372992*a(n-26) +1227008*a(n-28) -1025920*a(n-30) +3805952*a(n-32) -5750016*a(n-34) +3855360*a(n-36) +801280*a(n-38) -2436096*a(n-40) +253952*a(n-42) +1060864*a(n-44) -978944*a(n-46) +229376*a(n-48) +49152*a(n-50) -16384*a(n-52) for n>66

%e Some solutions for n=7

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

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

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

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

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

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

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

%Y Cf. A263666.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 23 2015