A264341 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

4, 13, 8, 49, 55, 16, 181, 490, 233, 32, 676, 3567, 4900, 987, 64, 2521, 28925, 70669, 49000, 4181, 128, 9409, 223356, 1243225, 1399783, 490000, 17711, 256, 35113, 1759250, 20386617, 53429620, 27726581, 4900000, 75025, 512, 131044, 13750304

Offset: 1

Author

R. H. Hardin, Nov 11 2015

Keywords

• nonn
• tabl

Comments

Table starts

....4......13.........49...........181..............676.................2521

....8......55........490..........3567............28925...............223356

...16.....233.......4900.........70669..........1243225.............20386617

...32.....987......49000.......1399783.........53429620...........1855980772

...64....4181.....490000......27726581.......2296230561.........168990466353

..128...17711....4900000.....549201567......98684484373.......15386771913704

..256...75025...49000000...10878455069....4241136597604.....1400983500645217

..512..317811..490000000..215477871383..182270189212469...127561175981852920

.1024.1346269.4900000000.4268134837381.7833376999538689.11614593343457551705

Examples

			Some solutions for n=3 k=4
..7..8..9..3..4....1..0..3..2..4....7..8..2..3..4....1..2..9..4..3
.12..5..0..1..2...12..6..7..9..8....5..6..0..1..9...12..6..0..7..8
.17.10.13..6.14...11.10..5.14.13...11.10.12.13.14...10.18..5.14.13
.15.16.18.11.19...16.15.17.18.19...15.17.16.18.19...15.17.16.11.19
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..143

Crossrefs

Column 1 is A000079(n+1).

Column 2 is A033887(n+1).

Row 1 is A097948.

Formula

Empirical for column k:

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

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

k=3: a(n) = 10*a(n-1)

k=4: a(n) = 19*a(n-1) +16*a(n-2)

k=5: a(n) = 43*a(n-1) -43*a(n-3) +a(n-4)

k=6: a(n) = 87*a(n-1) +374*a(n-2) -470*a(n-3) +207*a(n-4) +3*a(n-5)

k=7: a(n) = 191*a(n-1) +1102*a(n-2) -7594*a(n-3) -38349*a(n-4) +38507*a(n-5)

Empirical for row n:

n=1: a(n) = 4*a(n-1) -4*a(n-3) +a(n-4)

n=2: [order 14]

n=3: [order 34]