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A298187 T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero. 4
0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 0, 0, 3, 2, 2, 3, 0, 0, 5, 3, 3, 3, 5, 0, 0, 8, 5, 4, 4, 5, 8, 0, 0, 13, 8, 6, 5, 6, 8, 13, 0, 0, 21, 13, 9, 7, 7, 9, 13, 21, 0, 0, 34, 21, 14, 10, 10, 10, 14, 21, 34, 0, 0, 55, 34, 22, 15, 14, 14, 15, 22, 34, 55, 0, 0, 89, 55, 35, 23, 20, 19, 20, 23, 35, 55 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

Table starts

.0..0..0..0..0..0..0..0..0...0...0...0...0....0....0....0....0.....0.....0

.0..1..1..2..3..5..8.13.21..34..55..89.144..233..377..610..987..1597..2584

.0..1..1..2..3..5..8.13.21..34..55..89.144..233..377..610..987..1597..2584

.0..2..2..3..4..6..9.14.22..35..56..90.145..234..378..611..988..1598..2585

.0..3..3..4..5..7.10.15.23..36..57..91.146..235..379..612..989..1599..2586

.0..5..5..6..7.10.14.20.29..44..68.106.166..262..416..663.1059..1695..2718

.0..8..8..9.10.14.19.27.38..58..90.142.225..362..587..959.1572..2587..4270

.0.13.13.14.15.20.27.41.58..91.145.240.398..680.1157.2003.3476..6073.10620

.0.21.21.22.23.29.38.58.81.127.203.341.574.1019.1784.3212.5779.10480.18971

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..760

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = a(n-1) +a(n-2)

k=3: a(n) = a(n-1) +a(n-2)

k=4: a(n) = 2*a(n-1) -a(n-3) for n>4

k=5: a(n) = 2*a(n-1) -a(n-3) for n>4

k=6: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +2*a(n-4) -2*a(n-5) +a(n-7) for n>8

k=7: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +2*a(n-4) -2*a(n-5) +a(n-6) -a(n-7) +a(n-8) -a(n-10) +a(n-11) for n>12

EXAMPLE

Some solutions for n=7 k=4

..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0

..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0

..0..0..0..0. .0..0..1..1. .0..0..0..0. .1..1..1..1. .0..0..0..0

..0..0..0..0. .0..0..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1

..0..0..0..0. .0..0..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1

..0..0..0..0. .0..0..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0

..0..0..0..0. .0..0..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0

CROSSREFS

Column 2 is A000045(n-1).

Column 3 is A000045(n-1).

Column 4 is A001611(n-1).

Column 5 is A157725(n-1).

Sequence in context: A240753 A202149 A236533 * A298183 A098356 A298167

Adjacent sequences: A298184 A298185 A298186 * A298188 A298189 A298190

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 14 2018

STATUS

approved

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Last modified February 9 02:59 EST 2023. Contains 360153 sequences. (Running on oeis4.)