A053637 a(n) = ceiling(2^(n-1)/n).

1, 1, 2, 2, 4, 6, 10, 16, 29, 52, 94, 171, 316, 586, 1093, 2048, 3856, 7282, 13798, 26215, 49933, 95326, 182362, 349526, 671089, 1290556, 2485514, 4793491, 9256396, 17895698, 34636834, 67108864, 130150525, 252645136, 490853406

Offset: 1

Author

N. J. A. Sloane, Mar 23 2000

Keywords

• nonn

Comments

a(n) is a lower bound on (and may be equal to) the isometric path number of the hypercube (see Fitzpatrick et al.). - N. J. A. Sloane, Jan 19 2012.

References

• Fitzpatrick, Shannon L.; Nowakowski, Richard J.; Holton, Derek; and Caines, Ian; Covering hypercubes by isometric paths. Discrete Math. 240 (2001), no. 1-3, 253-260.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Programs

Magma

[Ceiling(2^(n-1)/n): n in [1..40]]; // Vincenzo Librandi, Dec 19 2011

Mathematica

Table[Ceiling[2^(n-1)/n],{n,1,40}] (* Vincenzo Librandi, Dec 19 2011 *)

PARI

vector(40, n, ceil(2^(n-1)/n) ) \\ G. C. Greubel, May 17 2019

Sage

[ceil(2^(n-1)/n) for n in [1..40]] # G. C. Greubel, May 17 2019