A177291 Number of permutations of 3 copies of 1..n with all adjacent differences <= 1 in absolute value.

1, 1, 20, 92, 506, 2288, 10010, 41618, 168284, 664958, 2584442, 9916688, 37679618, 142079906, 532572428, 1987037318, 7386724082, 27381500624, 101272019258, 373902595130, 1378571667644, 5077289249390, 18683930010890, 68709775705328, 252549056389394, 927895845621746

Offset

0,3

Comments

a(n) = (3n)!/6^n = A014606(n) for n<=2.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (7,-9,-22,28,36,-4,-8).

Formula

G.f.: (1 - 6*x + 22*x^2 - 17*x^3 + 36*x^4 - 50*x^5 - 20*x^6 - 12*x^7 - 8*x^8)/((1 - 2*x - 2*x^2)^2*(1 - 3*x - 3*x^2 + 2*x^3)). - Andrew Howroyd, Oct 27 2025

Crossrefs

Column k=3 of A331562.

Cf. A014606.

Sequence in context: A211140 A200431 A172200 * A169711 A281391 A071092

Adjacent sequences: A177288 A177289 A177290 * A177292 A177293 A177294

Keyword

nonn,easy

Author

R. H. Hardin, May 06 2010

Extensions

a(0)=1 prepended by Alois P. Heinz, Jan 21 2020

a(19)-a(20) from Alois P. Heinz, Jan 22 2020

Terms a(21) and beyond from Andrew Howroyd, May 14 2020

Status

approved