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Search: a297817 -id:a297817
Displaying 1-4 of 4 results found. page 1
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A297993 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 6 king-move adjacent elements, with upper left element zero. +10
7
0, 1, 1, 1, 4, 1, 2, 17, 17, 2, 3, 49, 48, 49, 3, 5, 166, 146, 146, 166, 5, 8, 573, 424, 466, 424, 573, 8, 13, 1933, 1274, 1446, 1446, 1274, 1933, 13, 21, 6538, 3820, 4648, 5100, 4648, 3820, 6538, 21, 34, 22165, 11529, 14888, 18189, 18189, 14888, 11529, 22165, 34 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Table starts
..0.....1.....1......2......3.......5........8........13.........21.........34
..1.....4....17.....49....166.....573.....1933......6538......22165......75089
..1....17....48....146....424....1274.....3820.....11529......34783.....104826
..2....49...146....466...1446....4648....14888.....47399.....150849.....480015
..3...166...424...1446...5100...18189....62390....213997.....735000....2520806
..5...573..1274...4648..18189...74675...290466...1134198....4475863...17501388
..8..1933..3820..14888..62390..290466..1276012...5745438...26249179..117931466
.13..6538.11529..47399.213997.1134198..5745438..30240388..163303980..862771193
.21.22165.34783.150849.735000.4475863.26249179.163303980.1056360518.6667346762
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..364
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6
k=3: [order 11] for n>13
k=4: [order 24] for n>27
k=5: [order 99] for n>104
EXAMPLE
Some solutions for n=6 k=4
..0..1..1..0. .0..0..0..0. .0..1..0..1. .0..0..0..1. .0..1..1..1
..1..0..1..0. .0..1..1..0. .0..1..0..1. .1..1..1..0. .0..0..0..0
..1..0..1..0. .0..1..1..0. .0..0..0..1. .0..0..0..1. .1..1..1..0
..1..0..1..0. .1..1..1..1. .0..1..0..1. .1..1..1..0. .0..0..1..1
..1..0..1..0. .0..1..1..0. .1..1..0..1. .1..0..0..1. .1..0..0..0
..0..1..0..0. .0..1..1..0. .1..0..0..1. .1..0..1..1. .1..1..1..1
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A297817.
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 10 2018
STATUS
approved
A298653 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero. +10
5
0, 1, 1, 1, 4, 1, 2, 17, 17, 2, 3, 49, 48, 49, 3, 5, 166, 146, 146, 166, 5, 8, 573, 424, 466, 424, 573, 8, 13, 1933, 1274, 1446, 1446, 1274, 1933, 13, 21, 6538, 3820, 4648, 5124, 4648, 3820, 6538, 21, 34, 22165, 11529, 14888, 18271, 18271, 14888, 11529, 22165, 34 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Table starts
..0.....1.....1......2......3.......5........8........13.........21.........34
..1.....4....17.....49....166.....573.....1933......6538......22165......75089
..1....17....48....146....424....1274.....3820.....11529......34783.....104826
..2....49...146....466...1446....4648....14888.....47399.....150849.....480015
..3...166...424...1446...5124...18271....62544....215035.....739962....2537660
..5...573..1274...4648..18271...75562...291784...1142188....4518674...17656883
..8..1933..3820..14888..62544..291784..1277500...5758443...26328879..118276552
.13..6538.11529..47399.215035.1142188..5758443..30337435..163931288..865848465
.21.22165.34783.150849.739962.4518674.26328879.163931288.1060912744.6689007779
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..287
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6
k=3: [order 11] for n>13
k=4: [order 24] for n>27
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..1. .0..0..1..0. .0..1..0..0. .0..1..1..0. .0..0..1..0
..1..1..1..0. .0..1..0..1. .1..0..1..0. .1..0..0..0. .1..0..1..0
..1..0..0..1. .1..1..0..1. .1..0..1..1. .0..1..1..1. .1..1..1..0
..0..1..1..1. .0..1..0..1. .1..0..0..0. .0..0..0..1. .1..0..1..0
..0..0..0..0. .0..0..1..1. .0..1..1..1. .1..1..1..0. .1..0..1..0
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A297817.
Column 3 is A297988.
Column 4 is A297989.
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 24 2018
STATUS
approved
A298846 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 6 or 8 king-move adjacent elements, with upper left element zero. +10
5
0, 1, 1, 1, 4, 1, 2, 17, 17, 2, 3, 49, 48, 49, 3, 5, 166, 146, 146, 166, 5, 8, 573, 424, 466, 424, 573, 8, 13, 1933, 1274, 1446, 1446, 1274, 1933, 13, 21, 6538, 3820, 4648, 5101, 4648, 3820, 6538, 21, 34, 22165, 11529, 14888, 18191, 18191, 14888, 11529, 22165, 34 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Table starts
..0.....1.....1......2......3.......5........8........13.........21.........34
..1.....4....17.....49....166.....573.....1933......6538......22165......75089
..1....17....48....146....424....1274.....3820.....11529......34783.....104826
..2....49...146....466...1446....4648....14888.....47399.....150849.....480015
..3...166...424...1446...5101...18191....62393....214017.....735090....2521128
..5...573..1274...4648..18191...74685...290474...1134326....4476521...17504192
..8..1933..3820..14888..62393..290474..1276034...5745665...26250580..117940632
.13..6538.11529..47399.214017.1134326..5745665..30242236..163316554..862848634
.21.22165.34783.150849.735090.4476521.26250580.163316554.1056423010.6667708149
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..337
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6
k=3: [order 11] for n>13
k=4: [order 24] for n>27
EXAMPLE
Some solutions for n=6 k=6
..0..1..1..1..0..0. .0..0..1..1..1..0. .0..1..0..1..0..1. .0..0..0..1..0..1
..1..0..1..0..1..0. .0..1..0..1..0..1. .1..0..1..1..1..0. .0..1..1..1..1..0
..0..1..1..1..0..1. .1..0..1..1..1..1. .1..1..1..1..1..1. .0..1..1..1..1..1
..1..1..1..1..1..1. .1..1..1..1..1..0. .1..0..1..1..1..0. .1..1..1..1..1..0
..0..1..1..1..0..1. .1..0..1..1..1..0. .0..1..0..1..0..1. .0..1..1..1..1..0
..1..0..1..0..1..0. .0..1..1..0..0..0. .0..0..1..1..1..0. .1..0..1..0..0..0
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A297817.
Column 3 is A297988.
Column 4 is A297989.
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 27 2018
STATUS
approved
A299607 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 6, 7 or 8 king-move adjacent elements, with upper left element zero. +10
5
0, 1, 1, 1, 4, 1, 2, 17, 17, 2, 3, 49, 48, 49, 3, 5, 166, 146, 146, 166, 5, 8, 573, 424, 466, 424, 573, 8, 13, 1933, 1274, 1446, 1446, 1274, 1933, 13, 21, 6538, 3820, 4648, 5125, 4648, 3820, 6538, 21, 34, 22165, 11529, 14888, 18273, 18273, 14888, 11529, 22165, 34 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Table starts
..0.....1.....1......2......3.......5........8........13.........21.........34
..1.....4....17.....49....166.....573.....1933......6538......22165......75089
..1....17....48....146....424....1274.....3820.....11529......34783.....104826
..2....49...146....466...1446....4648....14888.....47399.....150849.....480015
..3...166...424...1446...5125...18273....62547....215175.....740442....2539018
..5...573..1274...4648..18273...75970...292458...1146690....4552661...17798866
..8..1933..3820..14888..62547..292458..1284100...5779019...26461571..119048834
.13..6538.11529..47399.215175.1146690..5779019..30465069..164752420..870288036
.21.22165.34783.150849.740442.4552661.26461571.164752420.1069988410.6740006098
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..264
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6
k=3: [order 11] for n>13
k=4: [order 24] for n>27
EXAMPLE
Some solutions for n=6 k=6
..0..1..0..1..1..0. .0..0..1..1..0..1. .0..1..1..0..0..0. .0..0..1..0..1..0
..1..0..1..1..0..1. .1..1..0..1..1..0. .1..0..1..1..1..0. .1..1..0..0..0..1
..1..1..1..1..1..0. .0..0..1..1..1..1. .1..1..1..1..1..0. .0..0..0..0..0..0
..0..1..1..1..1..1. .1..1..1..1..1..0. .1..0..1..1..1..1. .0..0..0..0..0..1
..0..1..1..1..1..0. .1..1..1..1..1..0. .0..1..0..1..1..0. .1..1..0..0..1..0
..0..0..0..1..0..1. .0..0..1..0..0..0. .1..0..0..1..1..0. .0..0..1..0..0..1
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A297817.
Column 3 is A297988.
Column 4 is A297989.
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 14 2018
STATUS
approved
page 1

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Last modified August 30 07:09 EDT 2024. Contains 375532 sequences. (Running on oeis4.)