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 A266131 T(n,k) = Number of n X k integer arrays with each element equal to the number of horizontal, diagonal and antidiagonal neighbors exactly one smaller than itself. 12

%I #6 Apr 11 2022 13:18:29

%S 1,3,1,4,9,1,5,25,20,1,9,49,77,61,1,16,149,117,385,189,1,25,625,278,

%T 572,2099,544,1,39,2141,1959,3851,4336,9083,1629,1,64,5433,11044,

%U 44623,62104,19750,48188,4973,1,105,17269,36730,347576,1285961,326145,102201,249446

%N T(n,k) = Number of n X k integer arrays with each element equal to the number of horizontal, diagonal and antidiagonal neighbors exactly one smaller than itself.

%C Table starts

%C .1.....3.......4........5.........9.........16..........25.........39

%C .1.....9......25.......49.......149........625........2141.......5433

%C .1....20......77......117.......278.......1959.......11044......36730

%C .1....61.....385......572......3851......44623......347576....1650710

%C .1...189....2099.....4336.....62104....1285961....16386099..124675418

%C .1...544....9083....19750....326145...13689944...325554385.3901509248

%C .1..1629...48188...102201...4176690..311260836.10444421518

%C .1..4973..249446...620508..50677045.6688962679

%C .1.15040.1166325..3041449.367191341

%C .1.45739.6288299.16217839

%H R. H. Hardin, <a href="/A266131/b266131.txt">Table of n, a(n) for n = 1..97</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1),

%F k=2: [order 10],

%F k=3: [order 26] for n>27,

%F Empirical for row n:

%F n=1: a(n) = a(n-1) +a(n-3) +a(n-4),

%F n=2: [order 17],

%F n=3: [order 77].

%e Some solutions for n=4, k=4

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

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

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

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

%Y Column 2 is A196212.

%Y Row 1 is A195971.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Dec 21 2015

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Last modified August 12 10:37 EDT 2024. Contains 375092 sequences. (Running on oeis4.)