A089936 Number of 5 X n matrices with entries {0,1} without adjacent 0's in any row or column. 5th row of A089934.

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

Andrew Howroyd, Table of n, a(n) for n = 1..200

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

Row 5 of A089934.

Cf. A000045, A001333, A051736, A051737, A089935, A089937, A089938.

Sequence in context: A034270 A201427 A155646 * A196928 A266002 A367554

Adjacent sequences: A089933 A089934 A089935 * A089937 A089938 A089939

Keyword

nonn

Author

Marc LeBrun, Nov 15 2003

Status

approved