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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.

%I A265928 #4 Dec 18 2015 22:39:09
%S A265928 5,25,25,92,340,125,340,1740,4616,625,1252,9016,17936,62696,3125,4616,
%T A265928 44916,72772,174000,851496,15625,17012,223788,273616,542940,1671744,
%U A265928 11564952,78125,62696,1119424,1042020,1546496,4044156,15962560,157071768
%N 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.
%C A265928 Table starts
%C A265928 .......5...........25...........92.........340........1252........4616
%C A265928 ......25..........340.........1740........9016.......44916......223788
%C A265928 .....125.........4616........17936.......72772......273616.....1042020
%C A265928 .....625........62696.......174000......542940.....1546496.....4697060
%C A265928 ....3125.......851496......1671744.....4044156.....8821464....22093736
%C A265928 ...15625.....11564952.....15962560....30029860....51986544...112139348
%C A265928 ...78125....157071768....152267520...225444912...309447168...579039920
%C A265928 ..390625...2133318088...1451371264..1691502456..1904101280..3147755448
%C A265928 .1953125..28974227016..13834836992.12779302796.11662822720.16695518060
%C A265928 .9765625.393521606584.131883277312.96726712256.73936333840.93517706688
%H A265928 R. H. Hardin, <a href="/A265928/b265928.txt">Table of n, a(n) for n = 1..219</a>
%F A265928 Empirical for column k:
%F A265928 k=1: a(n) = 5*a(n-1)
%F A265928 k=2: [order 8]
%F A265928 k=3: [order 10] for n>13
%F A265928 k=4: [order 28] for n>32
%F A265928 k=5: [order 31] for n>39
%F A265928 k=6: [order 42] for n>50
%F A265928 k=7: [order 48] for n>55
%F A265928 Empirical for row n:
%F A265928 n=1: [linear recurrence of order 8] for n>9
%F A265928 n=2: [order 55] for n>59
%e A265928 Some solutions for n=3 k=4
%e A265928 ..2..0..0..1....1..1..3..0....1..0..3..2....0..1..1..4....3..4..1..0
%e A265928 ..4..4..1..0....2..4..4..1....4..3..0..1....3..0..0..2....0..1..3..3
%e A265928 ..3..3..0..1....0..3..1..0....1..0..3..4....4..1..1..4....4..4..1..0
%Y A265928 Column 1 is A000351.
%K A265928 nonn,tabl
%O A265928 1,1
%A A265928 _R. H. Hardin_, Dec 18 2015