A264550 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.

0, 1, 1, 1, 2, 0, 1, 6, 5, 0, 1, 16, 16, 10, 1, 3, 40, 36, 45, 21, 0, 3, 96, 172, 216, 133, 44, 0, 4, 240, 764, 1528, 1160, 400, 93, 1, 6, 608, 2728, 11728, 14852, 4640, 1204, 196, 0, 9, 1536, 9880, 66372, 163744, 105081, 23140, 3561, 413, 0, 12, 3840, 38818, 403920

Offset: 1

Author

R. H. Hardin, Nov 17 2015

Keywords

• nonn
• tabl

Comments

Table starts

.0...1.....1.......1.........1...........3.............3...............4

.1...2.....6......16........40..........96...........240.............608

.0...5....16......36.......172.........764..........2728............9880

.0..10....45.....216......1528.......11728.........66372..........403920

.1..21...133....1160.....14852......163744.......1573479........16103502

.0..44...400....4640....105081.....1994830......29691127.......480994368

.0..93..1204...23140....813473....25172836.....591482528.....15554895920

.1.196..3561..110592...6587227...316806958...11959837149....510948245264

.0.413.10554..501828..50597392..3939510885..234588752099..16034698666868

.0.870.31493.2390752.392445418.49105816488.4630258704238.508458281055496

Examples

			Some solutions for n=4 k=4
..1..2..5..6..7....1..2..3..4..7....1..2..3..7..8....1..5..3..6..8
..0.10..8..3..4....0.10..8.11.12....0.10.11.12..4....0..7..2.12..4
.11.12.15.14..9....5..6.13.17..9....5..6.13.17..9...11.15.13.14..9
.16.20.18.13.23...16.20.18.21.14...16.20.18.21.14...10.20.18.22.23
.21.22.17.24.19...15.22.23.24.19...15.22.23.24.19...21.16.17.24.19
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..198

Crossrefs

Row 1 is A080013(n+1).

Formula

Empirical for column k:

k=1: a(n) = a(n-3)

k=2: a(n) = 2*a(n-1) +a(n-4)

k=3: [order 15]

k=4: [order 10] for n>11

k=5: [order 84]

Empirical for row n:

n=1: a(n) = a(n-2) +a(n-3) +a(n-4) -a(n-6)

n=2: a(n) = 2*a(n-1) +8*a(n-4)

n=3: [order 70]

n=4: [order 56] for n>59