%I A002409 M4939 N1668
%S A002409 1,14,112,672,3360,14784,59136,219648,768768,2562560,8200192,25346048,
%T A002409 76038144,222265344,635043840,1778122752,4889837568,13231325184,
%U A002409 35283533824,92851404800,241413652480,620777963520,1580162088960
%N A002409 2^n*C(n+6,6). Number of 6D hypercubes in an (n+6)-dimensional hypercube.
%C A002409 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
%C A002409 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
%D A002409 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002409 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002409 H. Izbicki, Ueber Unterbaeume eines Baumes, Monatshefte f\"{u}r Mathematik, 
               74 (1970), 56-62.
%H A002409 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%H A002409 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 A002409 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.
%F A002409 a(n)=2*a(n-1)+A054849(n-1)
%F A002409 G.f.: 1/(1-2x)^7.
%p A002409 A002409:=-1/(2*z-1)**7; [S. Plouffe in his 1992 dissertation.]
%p A002409 seq(binomial(n+6,6)*2^n,n=0..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 16 2008
%o A002409 (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]
%Y A002409 Cf. A000079, A001787, A001788, A001789, A003472, A054849, A054851, A038207.
%Y A002409 For n>0, a(n) = 2 * A082140(n). First differences are in A006976.
%Y A002409 Sequence in context: A036395 A039630 A004408 this_sequence A155655 A007817 
               A044346
%Y A002409 Adjacent sequences: A002406 A002407 A002408 this_sequence A002410 A002411 
               A002412
%K A002409 easy,nonn
%O A002409 0,2
%A A002409 N. J. A. Sloane (njas(AT)research.att.com).
%E A002409 More terms from Henry Bottomley (se16(AT)btinternet.com) and James A. 
               Sellers (sellersj(AT)math.psu.edu), Apr 15 2000
%E A002409 Typo in definition corrected by Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 16 2008