cp's OEIS Frontend

A301669 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 horizontally or vertically adjacent elements, with upper left element zero.

%I A301669 #4 Mar 25 2018 11:38:18
%S A301669 0,1,1,1,3,1,2,10,10,2,3,23,30,23,3,5,61,118,118,61,5,8,162,407,564,
%T A301669 407,162,8,13,421,1498,2793,2793,1498,421,13,21,1103,5289,14394,21224,
%U A301669 14394,5289,1103,21,34,2890,19184,71564,146841,146841,71564,19184,2890,34,55
%N A301669 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 horizontally or vertically adjacent elements, with upper left element zero.
%C A301669 Table starts
%C A301669 ..0....1.....1.......2........3..........5...........8............13
%C A301669 ..1....3....10......23.......61........162.........421..........1103
%C A301669 ..1...10....30.....118......407.......1498........5289.........19184
%C A301669 ..2...23...118.....564.....2793......14394.......71564........359659
%C A301669 ..3...61...407....2793....21224.....146841.....1073621.......7703565
%C A301669 ..5..162..1498...14394...146841....1537496....15498505.....159497778
%C A301669 ..8..421..5289...71564..1073621...15498505...225780260....3307561389
%C A301669 .13.1103.19184..359659..7703565..159497778..3307561389...68862687289
%C A301669 .21.2890.68832.1808256.55506215.1631501428.48158543096.1434208027966
%H A301669 R. H. Hardin, <a href="/A301669/b301669.txt">Table of n, a(n) for n = 1..197</a>
%F A301669 Empirical for column k:
%F A301669 k=1: a(n) = a(n-1) +a(n-2)
%F A301669 k=2: a(n) = 2*a(n-1) +a(n-2) +2*a(n-3) -a(n-4)
%F A301669 k=3: [order 20]
%F A301669 k=4: [order 70]
%e A301669 Some solutions for n=5 k=4
%e A301669 ..0..0..1..1. .0..0..1..1. .0..0..0..1. .0..1..1..1. .0..0..1..1
%e A301669 ..0..1..0..1. .1..0..1..0. .1..1..1..1. .0..0..0..0. .1..1..0..1
%e A301669 ..1..1..0..0. .1..0..0..0. .1..0..0..0. .1..1..1..0. .0..0..0..0
%e A301669 ..1..0..1..1. .1..1..1..1. .0..1..1..0. .1..0..1..0. .0..1..0..1
%e A301669 ..1..0..0..1. .0..0..0..1. .0..0..1..0. .1..0..1..0. .0..1..1..1
%Y A301669 Column 1 is A000045(n-1).
%Y A301669 Column 2 is A185828.
%K A301669 nonn,tabl
%O A301669 1,5
%A A301669 _R. H. Hardin_, Mar 25 2018