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A054851 a(n) = 2^(n-7)*C(n,7). Number of 7D hypercubes in an n-dimensional hypercube. 15


%S 1,16,144,960,5280,25344,109824,439296,1647360,5857280,19914752,

%T 65175552,206389248,635043840,1905131520,5588385792,16066609152,

%U 45364543488,126012620800,344876646400,931166945280,2483111854080

%N a(n) = 2^(n-7)*C(n,7). Number of 7D hypercubes in an n-dimensional hypercube.

%C If X_1,X_2,...,X_n is a partition of a 2n-set X into 2-blocks then, for n>6, a(n) is equal to the number of (n+7)-subsets of X intersecting each X_i (i=1,2,...,n). - _Milan Janjic_, Jul 21 2007

%C With a different offset, number of n-permutations (n>=7) of 3 objects: u,v,z with repetition allowed, containing exactly seven (7) u's. Example: a(1)=16 because we have uuuuuuuv, uuuuuuvu, uuuuuvuu, uuuuvuuu, uuuvuuuu, uuvuuuuu, uvuuuuuu, vuuuuuuu, uuuuuuuz, uuuuuuzu, uuuuuzuu, uuuuzuuu, uuuzuuuu, uuzuuuuu, uzuuuuuu and zuuuuuuu. - _Zerinvary Lajos_, Jun 23 2008

%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative Functions</a>

%H M. Janjic and B. Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv 1301.4550, 2013

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (16,-112,448,-1120,1792,-1792,1024,-256).

%F a(n) = 2*a(n-1) + A002409(n-1).

%F a(n+8) = A082141(n+1)/2.

%F G.f.: x^7/(1-2*x)^8. [_Colin Barker_, Sep 04 2012]

%F a(n) = Sum_{i=7..n} binomial(i,7)*binomial(n,i). Example: for n=11, a(11) = 1*330 + 8*165 + 36*55 + 120*11 + 330*1 = 5280. - _Bruno Berselli_, Mar 23 2018

%p seq(binomial(n+7,7)*2^n,n=0..21); - _Zerinvary Lajos_, Jun 23 2008

%o (Sage) [lucas_number2(n, 2, 0)*binomial(n,7)/128 for n in xrange(7, 29)] [_Zerinvary Lajos_, Mar 10 2009]

%Y Cf. A000079, A001787, A001788, A001789, A003472, A054849, A002409, A038207.

%K nonn,easy

%O 7,2

%A _Henry Bottomley_, Apr 14 2000

%E More terms from _James A. Sellers_, Apr 15 2000

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Last modified January 18 16:40 EST 2019. Contains 319271 sequences. (Running on oeis4.)