0,2

N. Calkin and H. Wilf, The number of independent sets in a grid graph, SIAM J. Discrete Math., 11 (1998), pp. 54-60.

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.

H. Wilf, The number of independent sets in a grid graph (With N. Calkin)

a(n) = 2*a(n-1) + 6*a(n-2) - a(n-4)

G.f.:(1+3*x+x^2-x^3)/(1-2*x-6x^2+x^4) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 07 2006

There are 17 3x2 (0,1)-matrices with no consecutive 1's:

0 0, 0 1, 0 0, 0 0, 0 1, 1 0, 1 0, 1 0, 0 0, 0 1, 0 0, 0 1, 0 0, 0 1, 0 0, 1 0, 1 0

0 0, 0 0, 0 1, 0 0, 0 0, 0 0, 0 1, 0 0, 1 0, 1 0, 1 0, 1 0, 0 0, 0 0, 0 1, 0 0, 0 1

0 0, 0 0, 0 0, 0 1, 0 1, 0 0, 0 0, 0 1, 0 0, 0 0, 0 1, 0 1, 1 0, 1 0, 1 0, 1 0, 1 0

Cf. A051737.

Sequence in context: A026619 A007483 A128073 this_sequence A099528 A062229 A120893

Adjacent sequences: A051733 A051734 A051735 this_sequence A051737 A051738 A051739

easy,nonn,nice

Stephen G. Penrice (spenrice(AT)ets.org), Dec 06 1999

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 08 1999