cp's OEIS Frontend

A297595 T(n,k) = Number of n X k 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 5 neighboring 1s.

%I A297595 #6 Mar 01 2019 14:54:00
%S A297595 1,2,1,3,5,1,4,9,9,1,6,13,25,20,1,9,33,49,69,41,1,13,69,145,154,205,
%T A297595 85,1,19,121,443,752,577,597,178,1,28,253,1141,3145,3747,1977,1701,
%U A297595 369,1,41,529,3009,10131,23066,18577,6962,4949,769,1,60,1013,8455,37929,103673
%N A297595 T(n,k) = Number of n X k 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 5 neighboring 1s.
%C A297595 Table starts
%C A297595 .1...2.....3.....4.......6........9........13..........19...........28
%C A297595 .1...5.....9....13......33.......69.......121.........253..........529
%C A297595 .1...9....25....49.....145......443......1141........3009.........8455
%C A297595 .1..20....69...154.....752.....3145.....10131.......37929.......150388
%C A297595 .1..41...205...577....3747....23066....103673......514290......2834897
%C A297595 .1..85...597..1977...18577...163704....975485.....6551844.....50398161
%C A297595 .1.178..1701..6962...93150..1172288...9403199....85828150....919035936
%C A297595 .1.369..4949.24441..464697..8419996..90862063..1120526916..16723808887
%C A297595 .1.769.14389.85803.2320289.60354437.875241087.14592832760.303459238317
%H A297595 R. H. Hardin, <a href="/A297595/b297595.txt">Table of n, a(n) for n = 1..391</a>
%F A297595 Empirical for column k:
%F A297595 k=1: a(n) = a(n-1)
%F A297595 k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3) -a(n-4)
%F A297595 k=3: a(n) = a(n-1) +2*a(n-2) +10*a(n-3) +4*a(n-4) -8*a(n-5) -8*a(n-6)
%F A297595 k=4: [order 9]
%F A297595 k=5: [order 22]
%F A297595 k=6: [order 40]
%F A297595 k=7: [order 83]
%F A297595 Empirical for row n:
%F A297595 n=1: a(n) = a(n-1) +a(n-3)
%F A297595 n=2: a(n) = a(n-1) +4*a(n-3)
%F A297595 n=3: a(n) = a(n-1) +a(n-2) +8*a(n-3) +7*a(n-4) -8*a(n-6) -6*a(n-7)
%F A297595 n=4: [order 12]
%F A297595 n=5: [order 26]
%F A297595 n=6: [order 49]
%e A297595 Some solutions for n=6 k=4
%e A297595 ..0..0..0..0. .0..1..0..0. .1..0..0..0. .1..0..0..0. .0..0..1..0
%e A297595 ..0..1..1..0. .0..0..1..0. .0..1..0..0. .0..1..0..0. .0..1..0..0
%e A297595 ..0..0..0..0. .0..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..0
%e A297595 ..0..1..0..1. .0..0..1..1. .1..0..0..0. .0..0..0..0. .0..0..0..0
%e A297595 ..0..1..1..1. .0..0..0..0. .1..0..0..0. .0..0..0..0. .1..0..0..0
%e A297595 ..0..0..0..1. .1..1..0..0. .0..1..0..0. .0..0..0..0. .0..1..0..0
%Y A297595 Column 2 is A105309(n+1).
%Y A297595 Row 1 is A000930(n+1).
%Y A297595 Row 2 is A089977(n+1).
%K A297595 nonn,tabl
%O A297595 1,2
%A A297595 _R. H. Hardin_, Jan 01 2018