cp's OEIS Frontend

A298187 T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

%I A298187 #4 Jan 14 2018 09:40:34
%S A298187 0,0,0,0,1,0,0,1,1,0,0,2,1,2,0,0,3,2,2,3,0,0,5,3,3,3,5,0,0,8,5,4,4,5,
%T A298187 8,0,0,13,8,6,5,6,8,13,0,0,21,13,9,7,7,9,13,21,0,0,34,21,14,10,10,10,
%U A298187 14,21,34,0,0,55,34,22,15,14,14,15,22,34,55,0,0,89,55,35,23,20,19,20,23,35,55
%N A298187 T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
%C A298187 Table starts
%C A298187 .0..0..0..0..0..0..0..0..0...0...0...0...0....0....0....0....0.....0.....0
%C A298187 .0..1..1..2..3..5..8.13.21..34..55..89.144..233..377..610..987..1597..2584
%C A298187 .0..1..1..2..3..5..8.13.21..34..55..89.144..233..377..610..987..1597..2584
%C A298187 .0..2..2..3..4..6..9.14.22..35..56..90.145..234..378..611..988..1598..2585
%C A298187 .0..3..3..4..5..7.10.15.23..36..57..91.146..235..379..612..989..1599..2586
%C A298187 .0..5..5..6..7.10.14.20.29..44..68.106.166..262..416..663.1059..1695..2718
%C A298187 .0..8..8..9.10.14.19.27.38..58..90.142.225..362..587..959.1572..2587..4270
%C A298187 .0.13.13.14.15.20.27.41.58..91.145.240.398..680.1157.2003.3476..6073.10620
%C A298187 .0.21.21.22.23.29.38.58.81.127.203.341.574.1019.1784.3212.5779.10480.18971
%H A298187 R. H. Hardin, <a href="/A298187/b298187.txt">Table of n, a(n) for n = 1..760</a>
%F A298187 Empirical for column k:
%F A298187 k=1: a(n) = a(n-1)
%F A298187 k=2: a(n) = a(n-1) +a(n-2)
%F A298187 k=3: a(n) = a(n-1) +a(n-2)
%F A298187 k=4: a(n) = 2*a(n-1) -a(n-3) for n>4
%F A298187 k=5: a(n) = 2*a(n-1) -a(n-3) for n>4
%F A298187 k=6: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +2*a(n-4) -2*a(n-5) +a(n-7) for n>8
%F A298187 k=7: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +2*a(n-4) -2*a(n-5) +a(n-6) -a(n-7) +a(n-8) -a(n-10) +a(n-11) for n>12
%e A298187 Some solutions for n=7 k=4
%e A298187 ..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e A298187 ..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e A298187 ..0..0..0..0. .0..0..1..1. .0..0..0..0. .1..1..1..1. .0..0..0..0
%e A298187 ..0..0..0..0. .0..0..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1
%e A298187 ..0..0..0..0. .0..0..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1
%e A298187 ..0..0..0..0. .0..0..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0
%e A298187 ..0..0..0..0. .0..0..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0
%Y A298187 Column 2 is A000045(n-1).
%Y A298187 Column 3 is A000045(n-1).
%Y A298187 Column 4 is A001611(n-1).
%Y A298187 Column 5 is A157725(n-1).
%K A298187 nonn,tabl
%O A298187 1,12
%A A298187 _R. H. Hardin_, Jan 14 2018