A177282 Number of permutations of 2 copies of 1..n with all adjacent differences <= 1 in absolute value.

1, 1, 6, 12, 26, 48, 86, 148, 250, 416, 686, 1124, 1834, 2984, 4846, 7860, 12738, 20632, 33406, 54076, 87522, 141640, 229206, 370892, 600146, 971088, 1571286, 2542428, 4113770, 6656256, 10770086, 17426404, 28196554, 45623024, 73819646, 119442740, 193262458

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000 (terms n=1..197 from R. H. Hardin)

Formula

a(n) = (2n)!/2^n = A000680(n) for n<=2.

Maple

a:= proc(n) option remember; `if`(n<4, [1$2, 6, 12][n+1],
     ((8*n-31)*a(n-1) -(4*n-19)*a(n-2) -(3*n-10)*a(n-3)
      +(2*n-10)*a(n-4)) / (3*n-11))
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Jan 14 2016

Crossrefs

Column k=2 of A331562.

Cf. A000680.

Sequence in context: A065106 A264008 A283221 * A283139 A242843 A232935

Adjacent sequences: A177279 A177280 A177281 * A177283 A177284 A177285

Keyword

nonn,easy

Author

R. H. Hardin, May 06 2010

Status

approved