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Search: id:A000212
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| A000212 |
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[n^2/3].
(Formerly M2439 N0966)
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+0
17
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| 0, 0, 1, 3, 5, 8, 12, 16, 21, 27, 33, 40, 48, 56, 65, 75, 85, 96, 108, 120, 133, 147, 161, 176, 192, 208, 225, 243, 261, 280, 300, 320, 341, 363, 385, 408, 432, 456, 481, 507, 533, 560, 588, 616, 645, 675, 705, 736, 768, 800, 833, 867, 901, 936
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Let M_n be the n X n matrix of the following form [3 2 1 0 0 0 0 0 0 0 / 2 3 2 1 0 0 0 0 0 0 / 1 2 3 2 1 0 0 0 0 0 / 0 1 2 3 2 1 0 0 0 0 / 0 0 1 2 3 2 1 0 0 0 / 0 0 0 1 2 3 2 1 0 0 / 0 0 0 0 1 2 3 2 1 0 / 0 0 0 0 0 1 2 3 2 1 / 0 0 0 0 0 0 1 2 3 2 / 0 0 0 0 0 0 0 1 2 3]. Then for n>2 a(n) = det M_(n-2). - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 20 2002
Largest possible size for the directed Cayley graph on two generators having diameter n-2. - Ralf Stephan, Apr 27 2003
It seems that for n >= 2 a(n) = maximum number of non-overlapping 1x3 rectangles that can be packed into an n x n square. Rectangles can only be placed parallel to the sides of the square. Verified with http://lagrange.ime.usp.br/~lobato/packing/run/index.php [From Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Aug 03 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).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
C. K. Wong and D. Coppersmith, A combinatorial problem related to multimodule memory organizations, J. ACM 21 (1974), 392-402.
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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.
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FORMULA
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G.f.: x^2*(1+x)/((1-x)^2*(1-x^3)) - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 01 2002
Euler transform of length 3 sequence [ 3, -1, 1]. - Michael Somos Sep 25 2006
G.f.: x^2*(1-x^2)/((1-x)^3*(1-x^3)). a(-n)=a(n). - Michael Somos Sep 25 2006
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MAPLE
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A000212:=(-1+z-2*z**2+z**3-2*z**4+z**5)/(z**2+z+1)/(z-1)**3; [Conjectured by S. Plouffe in his 1992 dissertation. Gives sequence with an additional leading 1.]
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MATHEMATICA
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k0=k1=0; lst={k0, k1}; Do[kt=k1; k1=n^2-k1-k0; k0=kt; AppendTo[lst, k1], {n, 1, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
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PROGRAM
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(PARI) a(n)=n^2\3
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CROSSREFS
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Cf. A000290, A007590, A002620, A118015, A056827, A118013.
Adjacent sequences: A000209 A000210 A000211 this_sequence A000213 A000214 A000215
Sequence in context: A023660 A161339 A023562 this_sequence A094913 A020678 A014811
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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