A252829 - OEIS

%I #4 Dec 22 2014 12:59:56

%S 1,2,2,3,5,3,4,9,9,4,5,13,21,13,5,6,17,37,37,17,6,7,21,53,85,53,21,7,

%T 8,25,69,149,149,69,25,8,9,29,85,213,341,213,85,29,9,10,33,101,277,

%U 597,597,277,101,33,10,11,37,117,341,853,1365,853,341,117,37,11,12,41,133,405

%N T(n,k)=Number of nXk nonnegative integer arrays with upper left 0 and every value within 1 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down

%C Table starts

%C ..1..2...3...4....5....6.....7.....8......9.....10.....11.....12......13

%C ..2..5...9..13...17...21....25....29.....33.....37.....41.....45......49

%C ..3..9..21..37...53...69....85...101....117....133....149....165.....181

%C ..4.13..37..85..149..213...277...341....405....469....533....597.....661

%C ..5.17..53.149..341..597...853..1109...1365...1621...1877...2133....2389

%C ..6.21..69.213..597.1365..2389..3413...4437...5461...6485...7509....8533

%C ..7.25..85.277..853.2389..5461..9557..13653..17749..21845..25941...30037

%C ..8.29.101.341.1109.3413..9557.21845..38229..54613..70997..87381..103765

%C ..9.33.117.405.1365.4437.13653.38229..87381.152917.218453.283989..349525

%C .10.37.133.469.1621.5461.17749.54613.152917.349525.611669.873813.1135957

%H R. H. Hardin, <a href="/A252829/b252829.txt">Table of n, a(n) for n = 1..2563</a>

%F Empirical for column k:

%F k=1: a(n) = 1*n

%F k=2: a(n) = 4*n - 3 for n>1

%F k=3: a(n) = 16*n - 27 for n>2

%F k=4: a(n) = 64*n - 171 for n>3

%F k=5: a(n) = 256*n - 939 for n>4

%F k=6: a(n) = 1024*n - 4779 for n>5

%F k=7: a(n) = 4096*n - 23211 for n>6

%e Some solutions for n=4 k=4

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

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

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

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

%Y Diagonal is A002450

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Dec 22 2014