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A299728 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 64, 141, 64, 3, 5, 236, 1027, 1027, 236, 5, 8, 888, 7664, 14701, 7664, 888, 8, 13, 3336, 57471, 217069, 217069, 57471, 3336, 13, 21, 12512, 430401, 3224826, 6354153, 3224826, 430401, 12512, 21, 34, 46928, 3222716 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Table starts
..0.....1.......1.........2............3..............5................8
..1.....4......18........64..........236............888.............3336
..1....18.....141......1027.........7664..........57471...........430401
..2....64....1027.....14701.......217069........3224826.........47845523
..3...236....7664....217069......6354153......187530622.......5526277711
..5...888...57471...3224826....187530622....10997877289.....643936117646
..8..3336..430401..47845523...5526277711...643936117646...74902586591536
.13.12512.3222716.709688988.162794536467.37689687396652.8709586033088978
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 4*a(n-1) -2*a(n-2) +4*a(n-3) for n>4
k=3: a(n) = 6*a(n-1) +8*a(n-2) +20*a(n-3) +25*a(n-4) +11*a(n-5) +2*a(n-6) for n>7
k=4: [order 16] for n>17
k=5: [order 39] for n>40
k=6: [order 92] for n>93
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..1. .0..0..0..1. .0..0..0..0. .0..0..0..1. .0..0..0..0
..1..0..0..1. .0..0..0..1. .1..0..1..0. .0..1..1..1. .1..0..1..0
..1..0..1..0. .0..1..0..0. .1..0..1..1. .1..0..1..0. .1..0..1..1
..0..0..1..1. .0..1..1..0. .0..1..0..1. .1..1..1..0. .1..0..1..1
..1..1..0..1. .0..1..0..0. .1..1..0..0. .1..0..0..0. .1..1..0..0
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A231950(n-1).
Sequence in context: A299373 A299937 A299067 * A299839 A265178 A159766
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 17 2018
STATUS
approved

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Last modified July 17 22:17 EDT 2024. Contains 374377 sequences. (Running on oeis4.)