1,2

Slavik V. Jablan (jablans(AT)yahoo.com) observes that this is also number of generating rational knots and links. See reference.

Also the number of distinct binding configurations on an n-site one-dimensional linear lattice, where the molecules cannot touch each other. This number determines the order of recurrence for the partition function of binding to a two-dimensional n x m lattice.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

Jablan S. and Sazdanovic R., LinKnot: Knot Theory by Computer, World Scientific Press, 2007.

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Golomb, Polyominoes, Princeton Univ. Press 1994.

Y. Kong, General recurrence theory of ligand binding on a three-dimensional lattice, J. Chem. Phys. Vol. 111 (1999), pp. 4790-4799. (Table I)

W. E. Patton, Problem E1470, Amer. Math. Monthly, 69 (1962), 61-62.

T. D. Noe, Table of n, a(n) for n=1..500

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

C. G. Bower, Transforms (2)

S. V. Jablan, Geometry of Links, XII Yugoslav Geometric Seminar (Novi Sad, 1998), Novi Sad J. Math. 29 (1999), no. 3, 121-139.

Index entries for sequences related to dominoes

G.f.: (2-(x+x^2)^2)/(2*(1-x-x^2)) + (1+x+x^2)*(x^2+x^4)/(2*(1-x^2-x^4)).

"BIK" transform of x+x^2.

If F(n) is the n-th Fibonacci number, then a(2n)=(F(2n+1)+F(n+2))/2 and a(2n+1)=(F(2n+2)+F(n+1))/2.

A001224:=-(-1-z+2*z**2+z**3+z**4+z**5)/(z**4+z**2-1)/(z**2+z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]

a:= n-> (Matrix([[5, 4, 2, 2, 1, 1]]). Matrix(6, (i, j)-> if (i=j-1) then 1 elif j=1 then [1, 2, -1, 0, -1, -1][i] else 0 fi)^n)[1, 6]: seq (a(n), n=1..38); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 26 2008]

Essentially the same as A060312.

Sequence in context: A038000 A124280 A088518 this_sequence A102526 A050192 A007147

Adjacent sequences: A001221 A001222 A001223 this_sequence A001225 A001226 A001227

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms and formula from Christian G. Bower (bowerc(AT)usa.net), May 09 2000