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A297951
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 5 king-move adjacent elements, with upper left element zero.
8
0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 52, 56, 52, 3, 5, 174, 219, 219, 174, 5, 8, 604, 796, 948, 796, 604, 8, 13, 2048, 3079, 4258, 4258, 3079, 2048, 13, 21, 6948, 11614, 19561, 23840, 19561, 11614, 6948, 21, 34, 23652, 44076, 88441, 134642, 134642, 88441, 44076
OFFSET
1,5
COMMENTS
Table starts
..0.....1......1.......2........3.........5..........8..........13...........21
..1.....4.....18......52......174.......604.......2048........6948........23652
..1....18.....56.....219......796......3079......11614.......44076.......167210
..2....52....219.....948.....4258.....19561......88441......402245......1831311
..3...174....796....4258....23840....134642.....750733.....4222383.....23711537
..5...604...3079...19561...134642....938557....6423236....44289957....305715877
..8..2048..11614...88441...750733...6423236...53630550...451993176...3822668362
.13..6948..44076..402245..4222383..44289957..451993176..4667940027..48407285130
.21.23652.167210.1831311.23711537.305715877.3822668362.48407285130.616122541550
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) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6
k=3: [order 20] for n>21
k=4: [order 66] for n>69
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..1. .0..1..0..0. .0..1..1..1. .0..0..0..1. .0..1..0..0
..0..1..1..1. .0..1..1..1. .0..1..0..0. .1..0..1..1. .1..0..1..1
..1..1..0..1. .1..1..1..0. .0..1..0..1. .0..1..0..0. .1..1..0..0
..0..0..0..1. .0..0..1..0. .0..1..0..1. .0..1..0..1. .1..0..1..1
..1..1..1..0. .1..1..1..1. .0..1..0..1. .0..1..0..1. .1..0..0..0
CROSSREFS
Column 1 is A000045(n-1).
Sequence in context: A299228 A300040 A206359 * A298560 A298389 A299307
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 09 2018
STATUS
approved