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A253468 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock diagonal maximum minus antidiagonal minimum unequal to its neighbors horizontally, vertically, diagonally and antidiagonally 9

%I #4 Jan 01 2015 10:14:34

%S 81,540,540,3640,800,3640,24208,1400,1400,24208,162016,3072,2000,3072,

%T 162016,1081504,8536,2600,2600,8536,1081504,7227096,15888,5000,3744,

%U 5000,15888,7227096,48272160,44464,7784,7496,7496,7784,44464,48272160

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock diagonal maximum minus antidiagonal minimum unequal to its neighbors horizontally, vertically, diagonally and antidiagonally

%C Table starts

%C .........81....540...3640..24208.162016.1081504.7227096.48272160.322493040

%C ........540....800...1400...3072...8536...15888...44464....94416....273808

%C .......3640...1400...2000...2600...5000....7784...17000....28520.....65000

%C ......24208...3072...2600...3744...7496....8272...15680....31824.....94016

%C .....162016...8536...5000...7496...8000...12680...20000....33416.....68000

%C ....1081504..15888...7784...8272..12680...12800...20864....36352.....99200

%C ....7227096..44464..17000..15680..20000...20864...32000....41600.....80000

%C ...48272160..94416..28520..31824..33416...36352...41600....59904....119936

%C ..322493040.273808..65000..94016..68000...99200...80000...119936....128000

%C .2154281664.562320.111464.104272.116360..108800..124544...132352....202880

%H R. H. Hardin, <a href="/A253468/b253468.txt">Table of n, a(n) for n = 1..3360</a>

%F Empirical for diagonal and column k:

%F diagonal: a(n) = 16*a(n-4) for n>5

%F k=1: a(n) = 2*a(n-1) +27*a(n-2) +30*a(n-3) -7*a(n-4) -8*a(n-5) -75*a(n-6) -48*a(n-7) -16*a(n-8)

%F k=2: a(n) = 5*a(n-2) +8*a(n-4) -12*a(n-6) for n>7

%F k=3: a(n) = 5*a(n-2) -4*a(n-4) for n>6

%F k=4: a(n) = a(n-2) +16*a(n-4) -16*a(n-6) for n>8

%F k=5: a(n) = 5*a(n-2) -4*a(n-4) for n>6

%F k=6: a(n) = a(n-2) +16*a(n-4) -16*a(n-6) for n>8

%F k=7: a(n) = 5*a(n-2) -4*a(n-4) for n>6

%e Some solutions for n=4 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 01 2015

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Last modified March 4 05:23 EST 2024. Contains 370522 sequences. (Running on oeis4.)