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A269760
Number of n X 1 0..5 arrays with some element plus some horizontally or vertically adjacent neighbor totalling five exactly once.
2
0, 6, 60, 450, 3000, 18750, 112500, 656250, 3750000, 21093750, 117187500, 644531250, 3515625000, 19042968750, 102539062500, 549316406250, 2929687500000, 15563964843750, 82397460937500, 434875488281250
OFFSET
1,2
COMMENTS
Column 1 of A269767.
LINKS
FORMULA
Empirical: a(n) = 10*a(n-1) - 25*a(n-2).
Conjectures from Colin Barker, Mar 22 2018: (Start)
G.f.: 6*x^2 / (1 - 5*x)^2.
a(n) = 6*5^(n-2)*(n-1).
(End)
EXAMPLE
Some solutions for n=4:
..0. .2. .4. .2. .2. .5. .1. .0. .3. .1. .1. .5. .5. .2. .4. .0
..5. .3. .1. .5. .0. .1. .0. .4. .1. .1. .5. .0. .3. .4. .5. .0
..2. .3. .3. .0. .2. .4. .5. .2. .3. .4. .0. .3. .4. .1. .1. .5
..1. .0. .5. .0. .3. .5. .4. .3. .2. .0. .2. .3. .1. .1. .4. .3
CROSSREFS
Cf. A269767.
Sequence in context: A000911 A076100 A353040 * A043033 A179711 A061495
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 04 2016
STATUS
approved