A177298 Number of permutations of 4 copies of 1..n with all adjacent differences <= 1 in absolute value.

1, 1, 70, 780, 11482, 135040, 1543862, 16699380, 175280570, 1792874048, 17990831182, 177773616180, 1735220375914, 16769137076968, 160740670148270, 1530462874512756, 14491157235576770, 136575590461035368, 1282229192334549022, 11999276440029403356, 111987255233226452770

Offset

0,3

Comments

a(n) = (4n)!/24^n = A014608(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 (19,-74,-357,1533,3960,-3339,-6183,4698,729,-729).

Formula

G.f.: (1 - 18*x + 125*x^2 - 119*x^3 + 666*x^4 - 5901*x^5 - 1701*x^6 - 5382*x^7 - 8073*x^8 + 2835*x^9 - 1458*x^10 + 729*x^11)/((1 - 6*x - 12*x^2 + 9*x^3)^2*(1 - 7*x - 22*x^2 + 15*x^3 + 9*x^4)). - Andrew Howroyd, Oct 27 2025

Crossrefs

Cf. A014608.

Column k=4 of A331562.

Sequence in context: A232587 A027804 A212236 * A230897 A364862 A006037

Adjacent sequences: A177295 A177296 A177297 * A177299 A177300 A177301

Keyword

nonn,easy

Author

R. H. Hardin, May 06 2010

Extensions

a(0)=1 prepended by Alois P. Heinz, Jan 20 2020

a(12)-a(13) from Alois P. Heinz, Jan 21 2020

Terms a(14) and beyond from Andrew Howroyd, May 15 2020

Status

approved