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A089936
Number of 5 X n matrices with entries {0,1} without adjacent 0's in any row or column. 5th row of A089934.
6
13, 99, 827, 6743, 55447, 454385, 3729091, 30584687, 250916131, 2058249165, 16884649135, 138508056265, 1136221529549, 9320704799431, 76460212316453, 627222736888811, 5145271430670385, 42207992410219447, 346243111960194009
OFFSET
1,1
COMMENTS
Row/columns 1 through 7 are A000045, A001333, A051736, A051737, A089936, A089937, A089938.
Number of independent vertex sets in the grid graph P_5 X P_n. - Andrew Howroyd, Jun 06 2017
LINKS
Reinhardt Euler, The Fibonacci Number of a Grid Graph and a New Class of Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.2.6.
FORMULA
G.f.: x*(13 + 47*x - 37*x^2 - 129*x^3 + 68*x^4 + 49*x^5 - 23*x^6 - 3*x^7 + x^8) / (1 - 4*x - 36*x^2 + 105*x^4 - 15*x^5 - 64*x^6 + 20*x^7 + 4*x^8 - x^9) (conjectured). - Colin Barker, Jun 06 2017
The above conjecture is correct since the order of the recurrence is A089935(5) = 9. - Andrew Howroyd, Dec 24 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Marc LeBrun, Nov 15 2003
STATUS
approved