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Search: id:A003229
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| A003229 |
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a(n) = a(n-1) + 2*a(n-3).
(Formerly M2419)
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+0
7
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| 1, 1, 3, 5, 7, 13, 23, 37, 63, 109, 183, 309, 527, 893, 1511, 2565, 4351, 7373, 12503, 21205, 35951, 60957, 103367, 175269, 297183, 503917, 854455, 1448821, 2456655, 4165565, 7063207, 11976517, 20307647, 34434061, 58387095, 99002389
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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. E. Daykin and S. J. Tucker, Introduction to Dragon Curves. Unpublished, 1976.
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LINKS
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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 417
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MAPLE
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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
A003229:=-(1+2*z**2)/(-1+z+2*z**3); [Conjectured by S. Plouffe in his 1992 dissertation.]
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]
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CROSSREFS
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Essentially the same as A077949 and |A077974|. First differences of A003479. Partial sums of A052537. Equals |A077906(n)|+|A077906(n+1)|.
A155761 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 28 2009]
Sequence in context: A164939 A125272 A127443 this_sequence A077949 A077974 A126273
Adjacent sequences: A003226 A003227 A003228 this_sequence A003230 A003231 A003232
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 06 2000
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