Search: id:A003229
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%I A003229 M2419
%S A003229 1,1,3,5,7,13,23,37,63,109,183,309,527,893,1511,2565,4351,7373,12503,
%T A003229 21205,35951,60957,103367,175269,297183,503917,854455,1448821,2456655,
%U A003229 4165565,7063207,11976517,20307647,34434061,58387095,99002389
%N A003229 a(n) = a(n-1) + 2*a(n-3).
%C A003229 Equals eigensequence of an infinite lower triangular matrix with 1's 
               in the main diagonal, 0's in the subdiagonal and 2's in the subsubdiagonal. 
               (the triangle in the lower section of A155761). [From Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Jan 28 2009]
%D A003229 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003229 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.
%D A003229 D. E. Daykin and S. J. Tucker, Introduction to Dragon Curves. Unpublished, 
               1976.
%H A003229 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 A003229 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 A003229 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=417">
               Encyclopedia of Combinatorial Structures 417</a>
%p A003229 seq(add(binomial(n-2*k,k)*2^k,k=0..floor(n/3)),n=1..38); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 03 2007
%p A003229 A003229:=-(1+2*z**2)/(-1+z+2*z**3); [Conjectured by S. Plouffe in his 
               1992 dissertation.]
%p A003229 with(combstruct): SeqSeqSeqL := [T, {T=Sequence(S), S=Sequence(U, card 
               >= 1), U=Sequence(Z, card >=3)}, unlabeled]: seq(count(SeqSeqSeqL, 
               size=j), j=4..39); ;# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 04 2009]
%Y A003229 Essentially the same as A077949 and |A077974|. First differences of A003479. 
               Partial sums of A052537. Equals |A077906(n)|+|A077906(n+1)|.
%Y A003229 A155761 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 28 2009]
%Y A003229 Sequence in context: A164939 A125272 A127443 this_sequence A077949 A077974 
               A126273
%Y A003229 Adjacent sequences: A003226 A003227 A003228 this_sequence A003230 A003231 
               A003232
%K A003229 nonn,easy
%O A003229 0,3
%A A003229 N. J. A. Sloane (njas(AT)research.att.com).
%E A003229 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 06 2000

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