Search: id:A005710
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%I A005710 M0483
%S A005710 1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,11,14,18,23,29,36,44,53,64,78,96,119,
%T A005710 148,184,228,281,345,423,519,638,786,970,1198,1479,1824,2247,2766,3404,
%U A005710 4190,5160,6358,7837,9661,11908,14674,18078,22268,27428,33786,41623
%N A005710 a(n)=a(n-1)+a(n-8).
%C A005710 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.
%D A005710 E. Di Cera and Y. Kong, Theory of multivalent binding in one and two-dimensional 
               lattices, Biophysical Chemistry, Vol. 61 (1996), pp. 107-124.
%D A005710 Problem E3274, Amer. Math. Monthly, 95 (1988), 555.
%D A005710 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005710 T. D. Noe, <a href="b005710.txt">Table of n, a(n) for n=0..500</a>
%H A005710 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A005710 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A005710 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=381">
               Encyclopedia of Combinatorial Structures 381</a>
%p A005710 A005710:=-1/(-1+z+z**8); [S. Plouffe in his 1992 dissertation.]
%p A005710 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
%p A005710 M := Matrix(8, (i,j)-> if j=1 and member(i,[1,8]) then 1 elif (i=j-1) 
               then 1 else 0 fi); a := n -> (M^(n))[1,1]; seq (a(n), n=0..55); - 
               Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 27 2008
%Y A005710 Cf. A000045, A000079, A000930, A003269, A003520, A005708, A005709, A005711.
%Y A005710 Sequence in context: A079064 A123176 A017902 this_sequence A023358 A061379 
               A107322
%Y A005710 Adjacent sequences: A005707 A005708 A005709 this_sequence A005711 A005712 
               A005713
%K A005710 nonn,easy
%O A005710 0,9
%A A005710 N. J. A. Sloane (njas(AT)research.att.com).
%E A005710 More terms from Mohammad K. Azarian, azarian(AT)evansville.edu
%E A005710 Additional comments from Yong Kong (ykong(AT)curagen.com), Dec 16 2000

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