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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. 15

%I

%S 5,25,25,92,340,125,340,1740,4616,625,1252,9016,17936,62696,3125,4616,

%T 44916,72772,174000,851496,15625,17012,223788,273616,542940,1671744,

%U 11564952,78125,62696,1119424,1042020,1546496,4044156,15962560,157071768

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

%C Table starts

%C .......5...........25...........92.........340........1252........4616

%C ......25..........340.........1740........9016.......44916......223788

%C .....125.........4616........17936.......72772......273616.....1042020

%C .....625........62696.......174000......542940.....1546496.....4697060

%C ....3125.......851496......1671744.....4044156.....8821464....22093736

%C ...15625.....11564952.....15962560....30029860....51986544...112139348

%C ...78125....157071768....152267520...225444912...309447168...579039920

%C ..390625...2133318088...1451371264..1691502456..1904101280..3147755448

%C .1953125..28974227016..13834836992.12779302796.11662822720.16695518060

%C .9765625.393521606584.131883277312.96726712256.73936333840.93517706688

%H R. H. Hardin, <a href="/A265928/b265928.txt">Table of n, a(n) for n = 1..219</a>

%F Empirical for column k:

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

%F k=2: [order 8]

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

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

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

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

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

%F Empirical for row n:

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

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

%e Some solutions for n=3 k=4

%e ..2..0..0..1....1..1..3..0....1..0..3..2....0..1..1..4....3..4..1..0

%e ..4..4..1..0....2..4..4..1....4..3..0..1....3..0..0..2....0..1..3..3

%e ..3..3..0..1....0..3..1..0....1..0..3..4....4..1..1..4....4..4..1..0

%Y Column 1 is A000351.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 18 2015

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Last modified May 21 21:43 EDT 2022. Contains 353929 sequences. (Running on oeis4.)