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Search: id:A054849
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| A054849 |
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2^(n-5)*C(n,5). Number of 5D hypercubes in an n-dimensional hypercube. |
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16
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| 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; listen)
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OFFSET
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5,2
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COMMENT
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With 5 leading zeros, binomial transform of C(n,5) - Paul Barry (pbarry(AT)wit.ie), 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 R. Janjic (agnus(AT)blic.net), 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 (zerinvarylajos(AT)yahoo.com), Jun 13 2008
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LINKS
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Milan Janjic, Two Enumerative Functions
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FORMULA
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a(n)=2*a(n-1)+A003472(n-1)
G.f. 1/(1-2x)^6 E.g.f. exp(2x)(x^5/5!) (with 5 leading zeros) - Paul Barry (pbarry(AT)wit.ie), Apr 10 2003
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MAPLE
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seq(binomial(n+5, 5)*2^n, n=0..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 13 2008
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PROGRAM
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(Other) SAGE: [lucas_number2(n, 2, 0)*binomial(n, 5)/32 for n in xrange(5, 28)] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 10 2009]
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CROSSREFS
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Cf. A000079, A001787, A001788, A001789, A003472, A002409, A054851, A038207.
Equals 2 * A082139. First differences are in A006975.
Sequence in context: A085409 A111464 A004407 this_sequence A000761 A003209 A155645
Adjacent sequences: A054846 A054847 A054848 this_sequence A054850 A054851 A054852
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Apr 14 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 15 2000
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