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 A054849 a(n) = 2^(n-5)*binomial(n,5). Number of 5D hypercubes in an n-dimensional hypercube. 20
 1, 12, 84, 448, 2016, 8064, 29568, 101376, 329472, 1025024, 3075072, 8945664, 25346048, 70189056, 190513152, 508035072, 1333592064, 3451650048, 8820883456, 22284337152, 55710842880, 137950658560, 338606161920 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,2 COMMENTS With 5 leading zeros, binomial transform of binomial(n,5). - Paul Barry, Apr 10 2003 If X_1,X_2,...,X_n is a partition of a 2n-set X into 2-blocks then, for n>4, a(n) is equal to the number of (n+5)-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 five (5) u's. Example: a(1)=12 because we have uuuuuv, uuuuvu, uuuvuu, uuvuuu, uvuuuu, vuuuuu, uuuuuz, uuuuzu, uuuzuu, uuzuuu, uzuuuu and zuuuuu. - Zerinvary Lajos, Jun 13 2008 LINKS Milan Janjic, Two Enumerative Functions M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013. FORMULA a(n) = 2*a(n-1) + A003472(n-1). From Paul Barry, Apr 10 2003: (Start) O.g.f.: 1/(1-2*x)^6. E.g.f.: exp(2*x)(x^5/5!) (with 5 leading zeros). (End) a(n) = Sum_{i=5..n} binomial(i,5)*binomial(n,i). Example: for n=8, a(8) = 1*56 + 6*28 + 21*8 + 56*1 = 448. - Bruno Berselli, Mar 23 2018 MAPLE seq(binomial(n+5, 5)*2^n, n=0..22); # Zerinvary Lajos, Jun 13 2008 PROG (Sage) [lucas_number2(n, 2, 0)*binomial(n, 5)/32 for n in xrange(5, 28)] # Zerinvary Lajos, Mar 10 2009 CROSSREFS Cf. A000079, A001787, A001788, A001789, A003472, A002409, A054851, A038207. Equals 2 * A082139. First differences are in A006975. Sequence in context: A085409 A111464 A004407 * A000761 A174079 A003209 Adjacent sequences:  A054846 A054847 A054848 * A054850 A054851 A054852 KEYWORD easy,nonn AUTHOR Henry Bottomley, Apr 14 2000 EXTENSIONS More terms from James A. Sellers, Apr 15 2000 STATUS approved

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Last modified August 15 07:26 EDT 2018. Contains 313756 sequences. (Running on oeis4.)