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 A054851 a(n) = 2^(n-7)*C(n,7). Number of 7D hypercubes in an n-dimensional hypercube. 15
 1, 16, 144, 960, 5280, 25344, 109824, 439296, 1647360, 5857280, 19914752, 65175552, 206389248, 635043840, 1905131520, 5588385792, 16066609152, 45364543488, 126012620800, 344876646400, 931166945280, 2483111854080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 7,2 COMMENTS 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 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 LINKS Milan Janjic, Two Enumerative Functions M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550, 2013 Index entries for linear recurrences with constant coefficients, signature (16,-112,448,-1120,1792,-1792,1024,-256). FORMULA a(n) = 2*a(n-1) + A002409(n-1). a(n+8) = A082141(n+1)/2. G.f.: x^7/(1-2*x)^8. [Colin Barker, Sep 04 2012] 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 MAPLE seq(binomial(n+7, 7)*2^n, n=0..21); - Zerinvary Lajos, Jun 23 2008 PROG (Sage) [lucas_number2(n, 2, 0)*binomial(n, 7)/128 for n in xrange(7, 29)] [Zerinvary Lajos, Mar 10 2009] CROSSREFS Cf. A000079, A001787, A001788, A001789, A003472, A054849, A002409, A038207. Sequence in context: A128985 A004409 A319553 * A000762 A217711 A086952 Adjacent sequences:  A054848 A054849 A054850 * A054852 A054853 A054854 KEYWORD nonn,easy AUTHOR Henry Bottomley, Apr 14 2000 EXTENSIONS More terms from James A. Sellers, Apr 15 2000 STATUS approved

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Last modified October 22 18:55 EDT 2018. Contains 316500 sequences. (Running on oeis4.)