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Search: id:A002409
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| A002409 |
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2^n*C(n+6,6). Number of 6D hypercubes in an (n+6)-dimensional hypercube.
(Formerly M4939 N1668)
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+0
17
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| 1, 14, 112, 672, 3360, 14784, 59136, 219648, 768768, 2562560, 8200192, 25346048, 76038144, 222265344, 635043840, 1778122752, 4889837568, 13231325184, 35283533824, 92851404800, 241413652480, 620777963520, 1580162088960
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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If X_1,X_2,...,X_n is a partition of a 2n-set X into 2-blocks then, for n>5, a(n-6) is equal to the number of (n+6)-subsets of X intersecting each X_i (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), Jul 21 2007
With a different offset, number of n-permutations (n>=6) of 3 objects: u, v, z with repetition allowed, containing exactly six (6) u's. Example: a(1)=14 because we have uuuuuuv, uuuuuvu, uuuuvuu, uuuvuuu, uuvuuuu, uvuuuuu, vuuuuuu. uuuuuuz, uuuuuzu, uuuuzuu, uuuzuuu, uuzuuuu, uzuuuuu, zuuuuuu - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2008
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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).
H. Izbicki, Ueber Unterbaeume eines Baumes, Monatshefte f\"{u}r Mathematik, 74 (1970), 56-62.
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LINKS
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Milan Janjic, Two Enumerative Functions
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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a(n)=2*a(n-1)+A054849(n-1)
G.f.: 1/(1-2x)^7.
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MAPLE
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A002409:=-1/(2*z-1)**7; [S. Plouffe in his 1992 dissertation.]
seq(binomial(n+6, 6)*2^n, n=0..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2008
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PROGRAM
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(Other) SAGE: [lucas_number2(n, 2, 0)*binomial(n, 6)/64 for n in xrange(6, 29)] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 10 2009]
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CROSSREFS
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Cf. A000079, A001787, A001788, A001789, A003472, A054849, A054851, A038207.
For n>0, a(n) = 2 * A082140(n). First differences are in A006976.
Sequence in context: A036395 A039630 A004408 this_sequence A155655 A007817 A044346
Adjacent sequences: A002406 A002407 A002408 this_sequence A002410 A002411 A002412
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KEYWORD
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easy,nonn
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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 Henry Bottomley (se16(AT)btinternet.com) and James A. Sellers (sellersj(AT)math.psu.edu), Apr 15 2000
Typo in definition corrected by Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2008
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