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

Author

R. H. Hardin, May 06 2010

Keywords

• nonn
• easy

Links

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

Crossrefs

Column k=2 of A331562.

Cf. A000680.

Programs

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

Formula

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