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A036442
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a(n) = 2^((n-1)*(n+2)/2)
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12
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1, 4, 32, 512, 16384, 1048576, 134217728, 34359738368, 17592186044416, 18014398509481984, 36893488147419103232, 151115727451828646838272, 1237940039285380274899124224, 20282409603651670423947251286016, 664613997892457936451903530140172288
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OFFSET
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1,2
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COMMENTS
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Number of redundant paths for a fault-tolerant ATM switch.
Hankel transform (see A001906 for definition ) of A001850, A006139, A084601; also Hankel transform of the sequence 1, 0, 4, 0, 24, 0, 160, 0, 1120, ... (A059304 with interpolated zeros) . - Philippe Deléham, Jul 03 2005
Hankel transform of A109980 . Unsigned version of A127945 . [From Philippe Deléham, Dec 11 2008]
a(n) = the multiplicative Wiener index of the wheel graph with n+3 vertices. The multiplicative Wiener index of a connected simple graph G is defined as the product of the distances between all pairs of distinct vertices of G. The wheel graph with n+3 vertices has (n+3)(n+2)/2 pairs of distinct vertices, of which 2(n+2) are adjacent; each of the remaining (n+2)(n-1)/2 pairs are at distance 2; consequently, the multiplicative Wiener index is 2^((n-1)(n+2)/2) = a(n). - Emeric Deutsch, Aug 17 2015
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..80
P. Barry, Comparing two matrices of generalized moments defined by continued fraction expansions, arXiv preprint arXiv:1311.7161, 2013
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
I. Gutman, W. Linert, I. Lukovits, and Z. Tomovic, The multiplicative version of the Wiener index, J. Chem. Inf. Comput. Sci., 40, 2000, 113-116.
C. Lo and C. Chiu, A Fault-Tolerant Architecture for ATM Networks, 20th IEEE Conf. Local Computer Networks, 1995, pp. 29-36
Index to divisibility sequences
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FORMULA
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a(1) = 1, a(n) = a(n-1) * 2^n. - Vincenzo Librandi, Oct 24 2012
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MATHEMATICA
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Table[2^((n-1) * (n+2)/2), {n, 1, 30}] (* Vincenzo Librandi, Oct 24 2012 *)
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PROG
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(MAGMA) I:=[1]; [n le 1 select I[n] else Self(n-1)*2^n: n in [1..20]]; // Vincenzo Librandi, Oct 24 2012
(PARI) a(n)=2^((n-1)*(n+2)/2) \\ Charles R Greathouse IV, Oct 24 2012
(Maxima) A036442[n]:=2^((n-1)*(n+2)/2)$
makelist(A036442[n], n, 1, 30); /*Martin Ettl, Oct 29 2012*/
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CROSSREFS
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Sequence in context: A140179 A118990 A127945 * A186339 A086899 A219149
Adjacent sequences: A036439 A036440 A036441 * A036443 A036444 A036445
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KEYWORD
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easy,nonn
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AUTHOR
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Abdallah Rayhan (rayhan(AT)engr.uvic.ca)
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STATUS
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approved
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