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A002409 2^n*C(n+6,6). Number of 6D hypercubes in an (n+6)-dimensional hypercube.
(Formerly M4939 N1668)
20
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; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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 Janjic, 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, Jun 16 2008

REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..400

H. Izbicki, Über Unterbaeume eines Baumes, Monatshefte für Mathematik, 74 (1970), 56-62.

H. Izbicki, Über Unterbaeume eines Baumes, Monatshefte für Mathematik, 74 (1970), 56-62.

Milan Janjic, Two Enumerative Functions

M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550, 2013

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

FORMULA

G.f.: 1/(1-2x)^7.

a(n) = 2*a(n-1) + A054849(n-1).

MAPLE

A002409:=-1/(2*z-1)**7; # Simon Plouffe in his 1992 dissertation

seq(binomial(n+6, 6)*2^n, n=0..22); # Zerinvary Lajos, Jun 16 2008

PROG

(Sage) [lucas_number2(n, 2, 0)*binomial(n, 6)/64 for n in xrange(6, 29)] # Zerinvary Lajos, Mar 10 2009

(MAGMA) [2^n* Binomial(n+6, 6): n in [0..30]]; // Vincenzo Librandi, Oct 14 2011

CROSSREFS

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: A234800 A213348 A004408 * A155655 A007817 A044346

Adjacent sequences:  A002406 A002407 A002408 * A002410 A002411 A002412

KEYWORD

easy,nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Henry Bottomley and James A. Sellers, Apr 15 2000

Typo in definition corrected by Zerinvary Lajos, Jun 16 2008

STATUS

approved

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Last modified March 23 22:30 EDT 2017. Contains 283985 sequences.