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A304926 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5 or 7 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 4, 4, 8, 5, 5, 8, 16, 9, 15, 9, 16, 32, 22, 31, 31, 22, 32, 64, 45, 73, 87, 73, 45, 64, 128, 101, 191, 266, 266, 191, 101, 128, 256, 218, 466, 851, 1054, 851, 466, 218, 256, 512, 477, 1125, 2510, 4186, 4186, 2510, 1125, 477, 512, 1024, 1041, 2762, 7348, 16158 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
...1...2....4.....8.....16......32.......64.......128........256.........512
...2...4....5.....9.....22......45......101.......218........477........1041
...4...5...15....31.....73.....191......466......1125.......2762........6805
...8...9...31....87....266.....851.....2510......7348......21910.......65581
..16..22...73...266...1054....4186....16158.....63555.....251536......988178
..32..45..191...851...4186...21214...104451....524286....2629697....13159898
..64.101..466..2510..16158..104451...649029...4123792...26044218...164807242
.128.218.1125..7348..63555..524286..4123792..33757130..273455401..2220694647
.256.477.2762.21910.251536.2629697.26044218.273455401.2831764125.29378878160
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -2*a(n-4) for n>6
k=3: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) +2*a(n-4) -2*a(n-5) -7*a(n-6) -6*a(n-7) for n>9
k=4: [order 13] for n>18
k=5: [order 34] for n>41
k=6: [order 96] for n>103
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..1..1..1
..1..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1. .1..0..1..1
..0..0..0..0. .0..0..0..0. .0..0..0..0. .1..0..0..0. .1..1..1..1
..0..0..0..0. .0..0..1..0. .0..0..0..0. .0..0..0..1. .1..1..1..0
..0..0..1..0. .0..0..0..1. .0..0..1..0. .0..1..0..0. .1..0..1..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A052962 for n>2.
Sequence in context: A305340 A304604 A316420 * A306166 A317383 A033717
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, May 21 2018
STATUS
approved

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Last modified June 18 14:09 EDT 2024. Contains 373481 sequences. (Running on oeis4.)