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A301541 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 3 horizontally or vertically adjacent elements, with upper left element zero.

%I A301541 #4 Mar 23 2018 11:07:17
%S A301541 1,2,2,3,3,3,5,6,6,5,8,10,9,10,8,13,21,26,26,21,13,21,42,61,79,61,42,
%T A301541 21,34,86,154,212,212,154,86,34,55,179,374,603,658,603,374,179,55,89,
%U A301541 370,941,1841,2417,2417,1841,941,370,89,144,770,2357,5663,9037,10783,9037
%N A301541 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 3 horizontally or vertically adjacent elements, with upper left element zero.
%C A301541 Table starts
%C A301541 ..1...2....3.....5......8.....13......21.......34........55.........89
%C A301541 ..2...3....6....10.....21.....42......86......179.......370........770
%C A301541 ..3...6....9....26.....61....154.....374......941......2357.......5963
%C A301541 ..5..10...26....79....212....603....1841.....5663.....17379......53565
%C A301541 ..8..21...61...212....658...2417....9037....33526....125626.....477972
%C A301541 .13..42..154...603...2417..10783...47791...215362....990403....4616134
%C A301541 .21..86..374..1841...9037..47791..255406..1432328...8145489...46701775
%C A301541 .34.179..941..5663..33526.215362.1432328..9891331..68863154..484837793
%C A301541 .55.370.2357.17379.125626.990403.8145489.68863154.588765472.5132456266
%H A301541 R. H. Hardin, <a href="/A301541/b301541.txt">Table of n, a(n) for n = 1..241</a>
%F A301541 Empirical for column k:
%F A301541 k=1: a(n) = a(n-1) +a(n-2)
%F A301541 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F A301541 k=3: [order 20]
%F A301541 k=4: [order 62]
%e A301541 Some solutions for n=5 k=4
%e A301541 ..0..0..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
%e A301541 ..1..0..1..0. .1..1..1..0. .1..0..1..0. .1..1..1..0. .0..0..1..1
%e A301541 ..1..1..0..0. .0..0..0..1. .0..1..0..0. .0..0..0..0. .0..1..0..1
%e A301541 ..1..0..1..0. .1..0..1..0. .1..0..1..0. .1..0..0..0. .1..0..1..0
%e A301541 ..0..1..0..1. .0..1..1..1. .0..1..1..1. .1..0..1..0. .1..0..1..0
%Y A301541 Column 1 is A000045(n+1).
%Y A301541 Column 2 is A240513.
%K A301541 nonn,tabl
%O A301541 1,2
%A A301541 _R. H. Hardin_, Mar 23 2018