A302635 - OEIS

%I #4 Apr 10 2018 19:32:21

%S 1,2,2,3,3,4,5,9,6,8,8,17,8,10,16,13,25,14,19,21,32,21,65,25,33,42,42,

%T 64,34,185,47,65,101,82,86,128,55,385,83,149,257,248,189,179,256,89,

%U 649,150,304,691,719,657,469,370,512,144,1489,269,643,1734,2262,2303,1841,1029

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

%C Table starts

%C ...1...2....3....5.....8.....13.....21......34.......55.......89.......144

%C ...2...3....9...17....25.....65....185.....385......649.....1489......3929

%C ...4...6....8...14....25.....47.....83.....150......269......488.......876

%C ...8..10...19...33....65....149....304.....643.....1343.....2880......6038

%C ..16..21...42..101...257....691...1734....4502....11524....30121.....77399

%C ..32..42...82..248...719...2262...6460...19799....59002...179668....535412

%C ..64..86..189..657..2303...8981..30216..112431...408512..1512824...5441957

%C .128.179..469.1841..7695..35772.144266..652931..2863575.12800635..55765517

%C .256.370.1029.4892.24205.135125.642553.3499587.18446157.98898783.515558643

%H R. H. Hardin, <a href="/A302635/b302635.txt">Table of n, a(n) for n = 1..391</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1)

%F k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)

%F k=3: a(n) = a(n-1) +9*a(n-3) -4*a(n-4) +2*a(n-5) -10*a(n-6) +4*a(n-7) +4*a(n-9) for n>13

%F k=4: [order 21] for n>25

%F k=5: [order 29] for n>32

%F k=6: [order 54] for n>65

%F Empirical for row n:

%F n=1: a(n) = a(n-1) +a(n-2)

%F n=2: a(n) = a(n-1) +16*a(n-4) -8*a(n-5) for n>6

%F n=3: a(n) = a(n-1) +a(n-2) +2*a(n-4) -a(n-5) for n>7

%F n=4: [order 22] for n>23

%F n=5: [order 63] for n>64

%F n=6: [order 81] for n>86

%e Some solutions for n=5 k=4

%e ..0..0..1..0. .0..1..0..1. .0..1..0..1. .0..0..1..1. .0..1..0..1

%e ..1..1..1..0. .0..1..0..1. .0..1..0..0. .0..1..0..1. .0..0..0..1

%e ..0..0..0..0. .0..1..1..1. .0..1..0..1. .0..1..0..1. .0..1..0..1

%e ..0..1..1..1. .0..1..0..1. .0..0..1..0. .0..1..0..1. .0..1..0..1

%e ..0..1..0..0. .0..1..0..1. .1..1..1..0. .0..0..1..1. .0..1..1..0

%Y Column 1 is A000079(n-1).

%Y Column 2 is A240513.

%Y Row 1 is A000045(n+1).

%Y Row 2 is A302164.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Apr 10 2018