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A252961 T(n,k)=Number of (n+2)X(k+2) 0..4 arrays with every consecutive three elements in every row and diagonal having exactly two distinct values, and in every column and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order 16

%I

%S 60,119,140,223,120,297,603,155,185,711,1251,249,259,337,1543,3465,

%T 385,369,443,596,3461,7495,651,605,674,871,1186,7637,20977,1069,985,

%U 1027,1242,1681,2279,16689,46641,1757,1429,1551,1747,2201,2999,4165,35609

%N T(n,k)=Number of (n+2)X(k+2) 0..4 arrays with every consecutive three elements in every row and diagonal having exactly two distinct values, and in every column and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order

%C Table starts

%C ....60...119...223...603..1251..3465..7495..20977..46641.130201.295421.819671

%C ...140...120...155...249...385...651..1069...1757...2949...5045...8293..14403

%C ...297...185...259...369...605...985..1429...2421...3907...6027...9989..16623

%C ...711...337...443...674..1027..1551..2349...3759...5739...9054..14527..22950

%C ..1543...596...871..1242..1747..2822..4019...6133...9681..14784..22631..37118

%C ..3461..1186..1681..2201..3315..5100..6855..10888..16745..24270..38635..61564

%C ..7637..2279..2999..4275..6091..8767.12573..19192..27929..42791..65583.101848

%C .16689..4165..6103..8202.11027.16909.23471..33929..52191..76861.115015.182359

%C .35609..8552.11983.15026.21661.32096.42337..64393..96273.137384.210821.330363

%C .78429.16744.21749.29799.41149.57282.81323.118916.171809.254784.384825.580538

%H R. H. Hardin, <a href="/A252961/b252961.txt">Table of n, a(n) for n = 1..231</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 12] for n>15

%F k=2: [order 12] for n>14

%F k=3: [order 8] for n>10

%F k=4: [order 15] for n>17

%F k=5: [order 14] for n>16

%F k=6: [order 12] for n>15

%F k=7: [order 22] for n>25

%F Empirical for row n:

%F n=1: [linear recurrence of order 14] for n>16

%F n=2: [order 9] for n>12

%F n=3: [order 13] for n>15

%F n=4: [order 14] for n>16

%F n=5: [order 17] for n>19

%F n=6: [order 19] for n>21

%F n=7: [order 23] for n>25

%e Some solutions for n=2 k=4

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 25 2014

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Last modified January 29 00:42 EST 2022. Contains 350670 sequences. (Running on oeis4.)