A265928 T(n,k)=Number of nXk 0..4 arrays with the absolute differences of each element with its with horizontal and antidiagonal neighbors unique.

5, 25, 25, 92, 340, 125, 340, 1740, 4616, 625, 1252, 9016, 17936, 62696, 3125, 4616, 44916, 72772, 174000, 851496, 15625, 17012, 223788, 273616, 542940, 1671744, 11564952, 78125, 62696, 1119424, 1042020, 1546496, 4044156, 15962560, 157071768

Offset: 1

Author

R. H. Hardin, Dec 18 2015

Keywords

• nonn
• tabl

Comments

Table starts

.......5...........25...........92.........340........1252........4616

......25..........340.........1740........9016.......44916......223788

.....125.........4616........17936.......72772......273616.....1042020

.....625........62696.......174000......542940.....1546496.....4697060

....3125.......851496......1671744.....4044156.....8821464....22093736

...15625.....11564952.....15962560....30029860....51986544...112139348

...78125....157071768....152267520...225444912...309447168...579039920

..390625...2133318088...1451371264..1691502456..1904101280..3147755448

.1953125..28974227016..13834836992.12779302796.11662822720.16695518060

.9765625.393521606584.131883277312.96726712256.73936333840.93517706688

Examples

			Some solutions for n=3 k=4
..2..0..0..1....1..1..3..0....1..0..3..2....0..1..1..4....3..4..1..0
..4..4..1..0....2..4..4..1....4..3..0..1....3..0..0..2....0..1..3..3
..3..3..0..1....0..3..1..0....1..0..3..4....4..1..1..4....4..4..1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..219

Crossrefs

Column 1 is A000351.

Formula

Empirical for column k:

k=1: a(n) = 5*a(n-1)

k=2: [order 8]

k=3: [order 10] for n>13

k=4: [order 28] for n>32

k=5: [order 31] for n>39

k=6: [order 42] for n>50

k=7: [order 48] for n>55

Empirical for row n:

n=1: [linear recurrence of order 8] for n>9

n=2: [order 55] for n>59