A263679 Number of length n arrays of permutations of 0..n-1 with each element moved by -4 to 4 places and with no two consecutive decreases.

1, 2, 5, 17, 70, 277, 1009, 3487, 11708, 39905, 137984, 481005, 1680187, 5852468, 20335048, 70581031, 244962297, 850636578, 2955043270, 10266945188, 35669911963, 123914096828, 430440925456, 1495206245569, 5193902810084

Offset

1,2

Comments

Column 4 of A263683.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = a(n-1) +4*a(n-2) +5*a(n-3) +15*a(n-4) +32*a(n-5) +83*a(n-6) +177*a(n-7) +484*a(n-8) +31*a(n-9) -763*a(n-10) -877*a(n-11) -1255*a(n-12) -8*a(n-13) +689*a(n-14) -1926*a(n-15) -6341*a(n-16) +168*a(n-17) +4160*a(n-18) +5193*a(n-19) +14170*a(n-20) -90*a(n-21) -10484*a(n-22) +4691*a(n-23) +28799*a(n-24) -8336*a(n-25) -10253*a(n-26) +4897*a(n-27) -51433*a(n-28) -110*a(n-29) +39213*a(n-30) -19619*a(n-31) -38190*a(n-32) +25392*a(n-33) +3232*a(n-34) -6950*a(n-35) +33047*a(n-36) +5995*a(n-37) -24598*a(n-38) -929*a(n-39) +32120*a(n-40) -17156*a(n-41) -5644*a(n-42) +9174*a(n-43) -13742*a(n-44) -3448*a(n-45) +8503*a(n-46) +1927*a(n-47) -8426*a(n-48) +2497*a(n-49) +1593*a(n-50) -1252*a(n-51) +2298*a(n-52) +216*a(n-53) -1058*a(n-54) -131*a(n-55) +755*a(n-56) -128*a(n-57) -143*a(n-58) +32*a(n-59) -166*a(n-60) +13*a(n-61) +57*a(n-62) +4*a(n-63) -18*a(n-64) -2*a(n-65) +2*a(n-66) +4*a(n-68) -a(n-70)

Example

Some solutions for n=7
..3....1....1....3....0....3....3....2....2....4....3....0....0....1....4....2
..0....3....0....0....3....0....0....1....1....0....0....1....1....2....5....0
..2....0....3....4....4....2....6....5....3....6....1....6....3....0....0....4
..1....2....6....1....1....1....2....0....0....1....5....4....6....6....3....6
..6....6....4....2....5....5....5....6....6....2....2....5....2....3....1....1
..4....4....5....6....6....6....1....3....4....3....4....2....5....5....2....5
..5....5....2....5....2....4....4....4....5....5....6....3....4....4....6....3

Crossrefs

Cf. A263683.

Sequence in context: A326412 A183239 A263639 * A251177 A263640 A263680

Adjacent sequences: A263676 A263677 A263678 * A263680 A263681 A263682

Keyword

nonn

Author

R. H. Hardin, Oct 23 2015

Status

approved