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

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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, 2, 4, 10, 32, 122, 544, 2287, 7688, 25662, 79456, 256482, 809784, 2690604, 8874432, 30009480, 98599568, 332395712, 1084222064, 3637730112, 11844968640, 39726351272, 129526799072, 434837072968, 1418856843552, 4764806022144

1,2

Column 6 of A263666.

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

Some solutions for n=7

..6....3....2....3....1....5....6....5....4....1....5....6....2....2....2....4

..1....6....0....1....4....0....3....1....0....6....4....2....4....4....4....0

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

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

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

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

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

Cf. A263666.

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R. H. Hardin, Oct 23 2015

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