A036442 a(n) = 2^((n-1)*(n+2)/2).

1, 4, 32, 512, 16384, 1048576, 134217728, 34359738368, 17592186044416, 18014398509481984, 36893488147419103232, 151115727451828646838272, 1237940039285380274899124224, 20282409603651670423947251286016, 664613997892457936451903530140172288

Offset: 1

Author

Abdallah Rayhan (rayhan(AT)engr.uvic.ca)

Keywords

• easy
• nonn

Comments

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. - 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

Links

• 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 and J. Int. Seq. 17 (2014) # 14.5.1
• 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

Programs

Magma

I:=[1]; [n le 1 select I[n] else Self(n-1)*2^n: n in [1..20]]; // Vincenzo Librandi, Oct 24 2012

Mathematica

Table[2^((n-1) * (n+2)/2), {n, 1, 30}] (* Vincenzo Librandi, Oct 24 2012 *)

Maxima

A036442[n]:=2^((n-1)*(n+2)/2)$
makelist(A036442[n],n,1,30); /* Martin Ettl, Oct 29 2012 */

PARI

a(n)=2^((n-1)*(n+2)/2) \\ Charles R Greathouse IV, Oct 24 2012

Formula

a(1) = 1, a(n) = a(n-1) * 2^n. - Vincenzo Librandi, Oct 24 2012