A279709 - OEIS

%I #8 Mar 03 2023 05:44:10

%S 1,1,2,1,2,4,2,3,5,8,3,4,11,13,16,5,6,22,42,34,32,8,9,47,125,161,89,

%T 64,13,14,102,385,717,617,233,128,21,22,224,1195,3245,4121,2364,610,

%U 256,34,35,494,3751,14988,27346,23690,9057,1597,512,55,56,1089,11823,70220

%N T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A279709/b279709.txt">Table of n, a(n) for n = 1..221</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1)

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

%F k=3: a(n) = 5*a(n-1) -5*a(n-2) +2*a(n-3)

%F k=4: [order 8] for n>9

%F k=5: [order 12] for n>13

%F k=6: [order 32] for n>33

%F k=7: [order 60] for n>62

%F Empirical for row n:

%F n=1: a(n) = a(n-1) +a(n-2) for n>3

%F n=2: a(n) = 2*a(n-1) -a(n-3)

%F n=3: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +4*a(n-4) -a(n-5) -a(n-7) -a(n-8)

%F n=4: [order 23] for n>25

%F n=5: [order 56] for n>64

%e Table starts

%e ...1....1......1.......2.........3..........5............8............13

%e ...2....2......3.......4.........6..........9...........14............22

%e ...4....5.....11......22........47........102..........224...........494

%e ...8...13.....42.....125.......385.......1195.........3751.........11823

%e ..16...34....161.....717......3245......14988........70220........329692

%e ..32...89....617....4121.....27346.....187484......1302321.......9047660

%e ..64..233...2364...23690....230128....2342179.....24137862.....248664928

%e .128..610...9057..136181...1936687...29270275....447547408....6837220721

%e .256.1597..34699..782826..16300179..365809911...8297886949..187983779265

%e .512.4181.132938.4500021.137192011.4571688626.153848240903.5168463666199

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A001519.

%Y Row 1 is A000045(n-1).

%Y Row 2 is A001611.

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Dec 17 2016