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A302528
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
12
0, 1, 0, 1, 3, 0, 2, 7, 10, 0, 3, 10, 28, 23, 0, 5, 27, 42, 115, 61, 0, 8, 45, 100, 168, 497, 162, 0, 13, 98, 290, 539, 902, 2086, 421, 0, 21, 193, 730, 1977, 3683, 3256, 9091, 1103, 0, 34, 379, 1700, 5942, 23909, 17546, 15852, 40575, 2890, 0, 55, 778, 4246, 16733, 128242
OFFSET
1,5
COMMENTS
Table starts
.0....1......1......2.......3.........5..........8..........13...........21
.0....3......7.....10......27........45.........98.........193..........379
.0...10.....28.....42.....100.......290........730........1700.........4246
.0...23....115....168.....539......1977.......5942.......16733........49219
.0...61....497....902....3683.....23909.....128242......465323......1918153
.0..162...2086...3256...17546....182773....1275348.....5557469.....29725028
.0..421...9091..15852...92603...1551340...16130212....82774516....506265517
.0.1103..40575..77904..615351..18089458..303355178..1916999716..16636194027
.0.2890.172996.314276.3268978.155010391.3654880956.27228654766.305442540368
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) +2*a(n-3) -a(n-4)
k=3: [order 18]
k=4: [order 72]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
n=3: [order 15] for n>17
n=4: [order 68] for n>69
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..0. .0..1..0..0. .0..0..1..1. .0..1..1..1. .0..0..1..1
..1..1..0..0. .1..0..1..1. .1..1..0..0. .1..0..0..0. .1..0..0..1
..1..0..1..0. .0..1..0..1. .1..0..1..0. .1..1..1..1. .1..1..1..1
..0..0..1..1. .1..1..1..0. .1..0..0..1. .1..1..1..1. .0..0..1..1
..1..1..0..0. .0..0..0..1. .0..1..1..0. .1..0..0..1. .1..1..0..0
CROSSREFS
Column 2 is A185828.
Row 1 is A000045(n-1).
Row 2 is A302279.
Sequence in context: A223139 A302278 A302728 * A303410 A126671 A209437
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 09 2018
STATUS
approved