0,9

This comment covers a family of sequences which satisfy a recurrence of the form a(n) = a(n-1) + a(n-m), with a(n) = 1 for n = 0...m-1. The generating function is 1/(1-x-x^m). Also a(n) = sum(binomial(n-(m-1)*i, i), i=0..n/m). This family of binomial summations or recurrences gives the number of ways to cover (without overlapping) a linear lattice of n sites with molecules that are m sites wide. Special case: m=1: A000079; m=4: A003269; m=5: A003520; m=6: A005708; m=7: A005709; m=8: A005710.

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.

E. Di Cera and Y. Kong, Theory of multivalent binding in one and two-dimensional lattices, Biophysical Chemistry, Vol. 61 (1996), pp. 107-124.

Problem E3274, Amer. Math. Monthly, 95 (1988), 555.

T. D. Noe, Table of n, a(n) for n=0..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.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 381

A005710:=-1/(-1+z+z**8); [Conjectured by S. Plouffe in his 1992 dissertation.]

ZL:=[S, {a = Atom, b = Atom, S = Prod(X, Sequence(Prod(X, b))), X = Sequence(b, card >= 7)}, unlabelled]: seq(combstruct[count](ZL, size=n), n=7..62); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 26 2008

Cf. A000045, A000079, A000930, A003269, A003520, A005708, A005709, A005711.

Adjacent sequences: A005707 A005708 A005709 this_sequence A005711 A005712 A005713

Sequence in context: A079064 A123176 A017902 this_sequence A023358 A061379 A107322

nonn,easy

njas

More terms from Mohammad K. Azarian, azarian(AT)evansville.edu

Additional comments from Yong Kong (ykong(AT)curagen.com), Dec 16 2000