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A251028 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no 2X2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements 9

%I

%S 110,526,526,1966,2546,1966,6321,8207,8207,6321,18330,23404,20608,

%T 23404,18330,49481,60044,51347,51347,60044,49481,126955,144737,118871,

%U 119632,118871,144737,126955,314337,334167,272547,257578,257578,272547,334167

%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no 2X2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements

%C Table starts

%C .....110.....526....1966.....6321....18330....49481...126955....314337

%C .....526....2546....8207....23404....60044...144737...334167....755336

%C ....1966....8207...20608....51347...118871...272547...608267...1356939

%C ....6321...23404...51347...119632...257578...563271..1199576...2590598

%C ...18330...60044..118871...257578...516684..1078862..2203974...4638560

%C ...49481..144737..272547...563271..1078862..2160510..4230166...8587303

%C ..126955..334167..608267..1199576..2203974..4230166..7948184..15543033

%C ..314337..755336.1356939..2590598..4638560..8587303.15543033..29146692

%C ..759223.1690491.3017800..5601754..9823382.17595371.30783775..55366008

%C .1803024.3781186.6755296.12305560.21323795.37245814.63428115.109773400

%H R. H. Hardin, <a href="/A251028/b251028.txt">Table of n, a(n) for n = 1..391</a>

%F Empirical for column k:

%F k=1: a(n) = 7*a(n-1) -18*a(n-2) +17*a(n-3) +10*a(n-4) -39*a(n-5) +38*a(n-6) -17*a(n-7) +3*a(n-8)

%F k=2: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>13

%F k=3: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>14

%F k=4: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>14

%F k=5: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>14

%F k=6: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>14

%F k=7: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>14

%e Some solutions for n=4 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 29 2014

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Last modified September 30 03:02 EDT 2022. Contains 357095 sequences. (Running on oeis4.)