|
%I #4 Dec 31 2017 07:28:36
%S 1,2,1,4,10,1,7,31,29,1,12,68,110,87,1,21,218,314,531,280,1,37,729,
%T 1829,2281,2534,876,1,65,2097,8803,23348,14201,11405,2735,1,114,6139,
%U 34757,191192,270845,88808,53175,8583,1,200,18932,157673,1247716,3624914
%N T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.
%C Table starts
%C .1.....2.......4........7.........12...........21.............37
%C .1....10......31.......68........218..........729...........2097
%C .1....29.....110......314.......1829.........8803..........34757
%C .1....87.....531.....2281......23348.......191192........1247716
%C .1...280....2534....14201.....270845......3624914.......35049871
%C .1...876...11405....88808....3075264.....66289769......978288822
%C .1..2735...53175...573119...35919085...1272836591....28914051279
%C .1..8583..246040..3613793..414559944..23896899569...823340493402
%C .1.26900.1135117.22999331.4794512057.450529429259.23748019543354
%H R. H. Hardin, <a href="/A297506/b297506.txt">Table of n, a(n) for n = 1..242</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 2*a(n-1) +2*a(n-2) +5*a(n-3) -a(n-5) -a(n-6)
%F k=3: [order 11]
%F k=4: [order 18]
%F k=5: [order 50]
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
%F n=2: a(n) = 3*a(n-1) -2*a(n-2) +9*a(n-3) -6*a(n-4) -8*a(n-5)
%F n=3: [order 10]
%F n=4: [order 24]
%F n=5: [order 59]
%e Some solutions for n=4 k=4
%e ..1..1..1..1. .0..0..0..0. .0..0..1..0. .1..0..0..0. .0..0..0..0
%e ..0..0..0..0. .0..0..1..1. .0..0..0..1. .0..1..0..0. .0..0..0..0
%e ..1..0..0..0. .0..0..0..1. .0..0..1..0. .0..0..0..1. .0..0..0..1
%e ..1..1..0..0. .1..1..0..0. .1..1..0..0. .0..1..1..0. .0..0..1..1
%Y Column 2 is A295525.
%Y Row 1 is A005251(n+2).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Dec 31 2017
| 