A264546 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.

1, 16, 36, 216, 1160, 4640, 23140, 110592, 501828, 2390752, 11231244, 52348752, 246436064, 1155790856, 5415128884, 25420656744, 119225756880, 559133362408, 2623138509120, 12303725497848, 57710528607716, 270708963027848

Offset

1,2

Links

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

Formula

Empirical: a(n) = 9*a(n-2) + 54*a(n-3) + 60*a(n-4) - 54*a(n-5) - 279*a(n-6) - 270*a(n-7) + 64*a(n-8) - 864*a(n-9) - 1728*a(n-10) for n>11.

Empirical g.f.: x*(1 + 16*x + 27*x^2 + 18*x^3 - 88*x^4 - 154*x^5 + 19*x^6 - 90*x^7 - 628*x^8 - 72*x^9 + 192*x^10) / (1 - 9*x^2 - 54*x^3 - 60*x^4 + 54*x^5 + 279*x^6 + 270*x^7 - 64*x^8 + 864*x^9 + 1728*x^10). - Colin Barker, Jan 08 2019

Example

Some solutions for n=4:
..1..5..3..6..7....1..2..3..4..7....1..2..3..6..8....1..2..3..7..8
..0.10..2..9..4....0.10..8..9.12....0.10.11.12..4....0.10.11..9..4
.11.12.15..8.18....5..6.15.14.18....5.15..7.17..9....5..6.13.14.18
.16.17.20.13.14...16.11.20.13.23...16.20.18.13.14...16.20.12.21.23
.21.22.23.24.19...21.22.17.24.19...21.22.23.24.19...15.22.17.24.19

Crossrefs

Column 4 of A264550.

Sequence in context: A075369 A318425 A273373 * A218523 A300535 A053893

Adjacent sequences: A264543 A264544 A264545 * A264547 A264548 A264549

Keyword

nonn

Author

R. H. Hardin, Nov 17 2015

Status

approved