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A185818 1/5 the number of n X 2 0..4 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors. 1
1, 9, 76, 656, 5680, 49248, 426928, 3701360, 32089696, 278208816, 2411993584, 20911320416, 181295389360, 1571781109104, 13626909445216, 118141552910384, 1024254735084784, 8880006538838880, 76987211704914352, 667457928119357552 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 2 of A185825.
LINKS
FORMULA
Empirical: a(n) = 7*a(n-1) + 15*a(n-2) - 32*a(n-4) - 64*a(n-5).
Empirical g.f.: x*(1 + 2*x - 2*x^2 - 11*x^3 - 20*x^4) / (1 - 7*x - 15*x^2 + 32*x^4 + 64*x^5). - Colin Barker, Apr 16 2018
Empirical formulas verified (see link). - Robert Israel, Jul 23 2018
EXAMPLE
Some solutions for 4 X 2 with a(1,1)=0:
..0..2....0..0....0..0....0..0....0..0....0..0....0..3....0..0....0..0....0..0
..0..2....1..1....0..0....0..3....3..2....2..0....0..3....3..4....0..2....0..3
..1..1....1..1....4..4....4..3....3..2....2..0....2..3....3..4....4..2....3..3
..0..0....0..0....3..3....4..3....3..3....1..1....2..2....3..4....4..2....2..2
MAPLE
f:= gfun:-rectoproc({a(n) = 7*a(n-1) + 15*a(n-2) - 32*a(n-4) - 64*a(n-5), a(1)=1, a(2)=9, a(3)=76, a(4)=656, a(5)=5680}, a(n), remember):
map(f, [$1..30]); # Robert Israel, Jul 23 2018
PROG
(PARI) x='x+O('x^99); Vec(x*(1+2*x-2*x^2-11*x^3-20*x^4)/(1-7*x-15*x^2+32*x^4+64*x^5)) \\ Altug Alkan, Jul 23 2018
CROSSREFS
Cf. A185825.
Sequence in context: A056329 A190982 A082677 * A324354 A209667 A276754
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 05 2011
STATUS
approved

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Last modified May 30 04:46 EDT 2024. Contains 372958 sequences. (Running on oeis4.)