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A270111
Number of n X 1 0..7 arrays with some element plus some horizontally or vertically adjacent neighbor totalling seven exactly once.
2
0, 8, 112, 1176, 10976, 96040, 806736, 6588344, 52706752, 415065672, 3228288560, 24857821912, 189823367328, 1439493868904, 10851569165584, 81386768741880, 607687873272704, 4519678557465736, 33498794014157808, 247518866882388248
OFFSET
1,2
COMMENTS
Column 1 of A270118.
LINKS
FORMULA
Empirical: a(n) = 14*a(n-1) - 49*a(n-2).
Conjectures from Colin Barker, Mar 22 2018: (Start)
G.f.: 8*x^2 / (1 - 7*x)^2.
a(n) = 8*7^(n-2)*(n-1).
(End)
EXAMPLE
Some solutions for n=4:
..5. .5. .6. .5. .0. .4. .7. .4. .4. .5. .7. .0. .7. .7. .1. .5
..6. .5. .2. .2. .7. .3. .1. .3. .5. .2. .1. .4. .6. .2. .3. .0
..7. .2. .2. .2. .1. .3. .6. .1. .3. .4. .6. .3. .1. .6. .4. .7
..0. .3. .5. .3. .2. .6. .6. .5. .4. .0. .7. .6. .7. .1. .5. .7
CROSSREFS
Cf. A270118.
Sequence in context: A316818 A317568 A075851 * A053536 A139741 A067900
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 11 2016
STATUS
approved