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A303624 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 12
1, 1, 2, 1, 2, 4, 1, 12, 2, 8, 1, 20, 38, 3, 16, 1, 72, 68, 148, 6, 32, 1, 168, 362, 325, 616, 10, 64, 1, 496, 1283, 3591, 1870, 2520, 21, 128, 1, 1296, 5411, 19467, 37910, 10741, 10288, 42, 256, 1, 3616, 22516, 160807, 350410, 398859, 62207, 42100, 86, 512, 1, 9760 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Table starts
...1..1......1.......1.........1...........1.............1................1
...2..2.....12......20........72.........168...........496.............1296
...4..2.....38......68.......362........1283..........5411............22516
...8..3....148.....325......3591.......19467........160807..........1173612
..16..6....616....1870.....37910......350410.......5249045.........70522741
..32.10...2520...10741....398859.....6446485.....179884814.......4470005178
..64.21..10288...62207...4288358...122517773....6323564388.....290118140045
.128.42..42100..363485..46208517..2348299355..224091914399...18955122420980
.256.86.172268.2135551.499581127.45211204167.7966090548780.1240883902751147
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: a(n) = 5*a(n-1) -5*a(n-2) +8*a(n-3) -12*a(n-4) +4*a(n-5) -4*a(n-6) for n>8
k=4: [order 22] for n>24
k=5: [order 62] for n>65
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 2*a(n-1) +4*a(n-2) -4*a(n-3) -4*a(n-4)
n=3: [order 16] for n>17
n=4: [order 43] for n>44
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..1. .0..0..0..1
..0..0..1..1. .0..0..0..0. .0..0..1..1. .1..0..0..0. .0..0..0..1
..0..0..1..1. .1..1..0..0. .1..1..1..1. .0..0..0..1. .1..0..0..0
..1..1..1..1. .0..1..1..1. .1..1..1..1. .0..0..0..1. .0..0..0..1
..0..1..1..1. .0..1..1..1. .0..1..1..0. .1..0..0..0. .0..0..0..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240513(n-2).
Row 2 is A302368.
Sequence in context: A302367 A303084 A302889 * A121439 A307448 A305350
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 27 2018
STATUS
approved

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Last modified June 19 13:19 EDT 2024. Contains 373503 sequences. (Running on oeis4.)