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A279709 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.

%I A279709 #8 Mar 03 2023 05:44:10
%S A279709 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 A279709 64,13,14,102,385,717,617,233,128,21,22,224,1195,3245,4121,2364,610,
%U A279709 256,34,35,494,3751,14988,27346,23690,9057,1597,512,55,56,1089,11823,70220
%N A279709 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 A279709 R. H. Hardin, <a href="/A279709/b279709.txt">Table of n, a(n) for n = 1..221</a>
%F A279709 Empirical for column k:
%F A279709 k=1: a(n) = 2*a(n-1)
%F A279709 k=2: a(n) = 3*a(n-1) -a(n-2)
%F A279709 k=3: a(n) = 5*a(n-1) -5*a(n-2) +2*a(n-3)
%F A279709 k=4: [order 8] for n>9
%F A279709 k=5: [order 12] for n>13
%F A279709 k=6: [order 32] for n>33
%F A279709 k=7: [order 60] for n>62
%F A279709 Empirical for row n:
%F A279709 n=1: a(n) = a(n-1) +a(n-2) for n>3
%F A279709 n=2: a(n) = 2*a(n-1) -a(n-3)
%F A279709 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 A279709 n=4: [order 23] for n>25
%F A279709 n=5: [order 56] for n>64
%e A279709 Table starts
%e A279709 ...1....1......1.......2.........3..........5............8............13
%e A279709 ...2....2......3.......4.........6..........9...........14............22
%e A279709 ...4....5.....11......22........47........102..........224...........494
%e A279709 ...8...13.....42.....125.......385.......1195.........3751.........11823
%e A279709 ..16...34....161.....717......3245......14988........70220........329692
%e A279709 ..32...89....617....4121.....27346.....187484......1302321.......9047660
%e A279709 ..64..233...2364...23690....230128....2342179.....24137862.....248664928
%e A279709 .128..610...9057..136181...1936687...29270275....447547408....6837220721
%e A279709 .256.1597..34699..782826..16300179..365809911...8297886949..187983779265
%e A279709 .512.4181.132938.4500021.137192011.4571688626.153848240903.5168463666199
%e A279709 Some solutions for n=4 k=4
%e A279709 ..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
%e A279709 ..0..0..1..0. .0..1..1..0. .0..1..0..0. .0..1..0..1. .0..1..1..0
%e A279709 ..1..0..1..1. .0..0..1..1. .0..0..1..1. .0..1..0..1. .0..0..0..1
%e A279709 ..0..1..0..1. .0..1..0..1. .1..0..0..1. .0..1..0..1. .1..1..0..1
%Y A279709 Column 1 is A000079(n-1).
%Y A279709 Column 2 is A001519.
%Y A279709 Row 1 is A000045(n-1).
%Y A279709 Row 2 is A001611.
%K A279709 nonn,tabl
%O A279709 1,3
%A A279709 _R. H. Hardin_, Dec 17 2016