cp's OEIS Frontend

A303197 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A303197 #4 Apr 19 2018 13:36:36
%S A303197 1,2,2,3,3,4,5,9,6,8,8,17,12,10,16,13,25,23,23,21,32,21,65,43,46,62,
%T A303197 42,64,34,185,105,97,185,122,86,128,55,385,233,283,523,497,305,179,
%U A303197 256,89,649,479,687,2106,1751,1357,793,370,512,144,1489,968,1642,7425,8250,5573
%N A303197 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A303197 Table starts
%C A303197 ...1...2....3.....5.....8.....13......21.......34........55.........89
%C A303197 ...2...3....9....17....25.....65.....185......385.......649.......1489
%C A303197 ...4...6...12....23....43....105.....233......479.......968.......2146
%C A303197 ...8..10...23....46....97....283.....687.....1642......3949......10169
%C A303197 ..16..21...62...185...523...2106....7425....23976.....77199.....278516
%C A303197 ..32..42..122...497..1751...8250...34801...138014....547379....2363422
%C A303197 ..64..86..305..1357..5573..32223..164295...791150...3806973...20061588
%C A303197 .128.179..793..4207.21575.159440.1053249..6303961..38494616..258640170
%C A303197 .256.370.1757.12167.76833.703465.5803057.43287208.332058205.2785202370
%H A303197 R. H. Hardin, <a href="/A303197/b303197.txt">Table of n, a(n) for n = 1..241</a>
%F A303197 Empirical for column k:
%F A303197 k=1: a(n) = 2*a(n-1)
%F A303197 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F A303197 k=3: [order 7] for n>11
%F A303197 k=4: [order 42] for n>43
%F A303197 k=5: [order 33] for n>37
%F A303197 Empirical for row n:
%F A303197 n=1: a(n) = a(n-1) +a(n-2)
%F A303197 n=2: a(n) = a(n-1) +16*a(n-4) -8*a(n-5) for n>6
%F A303197 n=3: [order 18] for n>19
%F A303197 n=4: [order 70] for n>71
%e A303197 Some solutions for n=5 k=4
%e A303197 ..0..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..1..0
%e A303197 ..1..1..1..0. .0..1..1..1. .0..0..0..1. .0..1..0..0. .0..1..0..1
%e A303197 ..1..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
%e A303197 ..1..0..1..0. .0..0..0..1. .0..1..1..1. .0..1..0..1. .0..0..0..1
%e A303197 ..1..0..0..1. .1..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..1..1
%Y A303197 Column 1 is A000079(n-1).
%Y A303197 Column 2 is A240513.
%Y A303197 Row 1 is A000045(n+1).
%Y A303197 Row 2 is A302164.
%K A303197 nonn,tabl
%O A303197 1,2
%A A303197 _R. H. Hardin_, Apr 19 2018