A264515 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

1, 1, 9, 36, 144, 576, 2116, 8281, 31329, 121801, 467856, 1809025, 6969600, 26884225, 103632400, 399560121, 1540484001, 5939322489, 22899558276, 88289802496, 340406901136, 1312449766884, 5060209759081, 19509827162049, 75220946346001

Offset

1,3

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +7*a(n-2) -17*a(n-3) -5*a(n-4) +60*a(n-5) +8*a(n-6) -24*a(n-7) -36*a(n-8) +36*a(n-11) +24*a(n-12) -8*a(n-13) -60*a(n-14) +5*a(n-15) +17*a(n-16) -7*a(n-17) -3*a(n-18) +a(n-19).

Conjecture: a(n) = A264507(n)^2. - Bruce Nye, Feb 11 2026

Example

Some solutions for n=4:
..4..5..0..7....4..5..0..1....4..5..6..7....6..5..0..1....4..7..0..1
..8..1..2..3....8.11..2..3....0..1..2..3...10.11..2..3...10.11..2..3
.14.15..6..9...14.15..6..7...14.15..8..9....4.15..8..7...14..5..6..9
.18.19.10.11...18..9.10.19...18.19.10.11...16..9.18.19....8.17.18.19
.12.13.16.17...12.13.16.17...12.13.16.17...12.13.14.17...12.13.16.15

Crossrefs

Column 3 of A264520.

Cf. A264507.

Sequence in context: A034557 A285241 A231431 * A002063 A285674 A075674

Adjacent sequences: A264512 A264513 A264514 * A264516 A264517 A264518

Keyword

nonn

Author

R. H. Hardin, Nov 16 2015

Status

approved