Search: id:A005708
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%I A005708 M0496
%S A005708 1,1,1,1,1,1,2,3,4,5,6,7,9,12,16,21,27,34,43,55,71,92,119,153,196,251,
               322,414,
%T A005708 533,686,882,1133,1455,1869,2402,3088,3970,5103,6558,8427,10829,13917,
               17887,
%U A005708 22990,29548,37975,48804,62721,80608,103598,133146,171121,219925,282646
%N A005708 a(n)=a(n-1)+a(n-6).
%C A005708 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 A005708 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 A005708 Problem E3274, Amer. Math. Monthly, 95 (1988), 555.
%D A005708 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005708 T. D. Noe, <a href="b005708.txt">Table of n, a(n) for n=0..500</a>
%H A005708 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 A005708 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 A005708 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=379">
               Encyclopedia of Combinatorial Structures 379</a>
%F A005708 a(n) = term (1,1) in the 6x6 matrix [1,1,0,0,0,0; 0,0,1,0,0,0; 0,0,0,
               1,0,0; 0,0,0,0,1,0; 0,0,0,0,0,1]; 1,0,0,0,0,0]^n. - Alois P. Heinz 
               (heinz(AT)hs-heilbronn.de), Jul 27 2008
%p A005708 with(combstruct): SeqSetU := [S, {S=Sequence(U), U=Set(Z, card > 5)}, 
               unlabeled]: seq(count(SeqSetU, size=j), j=6..59); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Oct 10 2006
%p A005708 A005708:=-1/(-1+z+z**6); [S. Plouffe in his 1992 dissertation.]
%p A005708 ZL:=[S, {a = Atom, b = Atom, S = Prod(X,Sequence(Prod(X,b))), X = Sequence(b,
               card >= 5)}, unlabelled]: seq(combstruct[count](ZL, size=n), n=5..58); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 26 2008
%p A005708 M := Matrix(6, (i,j)-> if j=1 and member(i,[1,6]) then 1 elif (i=j-1) 
               then 1 else 0 fi); a := n -> (M^(n))[1,1]; seq (a(n), n=0..53); - 
               Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 27 2008
%Y A005708 Cf. A000045, A000079, A000930, A003269, A003520, A005709, A005710, A005711.
%Y A005708 Sequence in context: A126327 A098132 A017900 this_sequence A085793 A143286 
               A160339
%Y A005708 Adjacent sequences: A005705 A005706 A005707 this_sequence A005709 A005710 
               A005711
%K A005708 nonn,easy
%O A005708 0,7
%A A005708 N. J. A. Sloane (njas(AT)research.att.com).
%E A005708 More terms from Mohammad K. Azarian (ma3(AT)evansville.edu)
%E A005708 Additional comments from Yong Kong (ykong(AT)curagen.com), Dec 16 2000

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