A126883 a(n) = (2^0)*(2^1)*(2^2)*(2^3)...(2^n)-1 = 2^T(n) - 1 where T(n) = A000217(n) is the n-th triangular number.

0, 1, 7, 63, 1023, 32767, 2097151, 268435455, 68719476735, 35184372088831, 36028797018963967, 73786976294838206463, 302231454903657293676543, 2475880078570760549798248447, 40564819207303340847894502572031, 1329227995784915872903807060280344575

Offset: 0

Author

Marco Matosic, Dec 29 2006

Keywords

• nonn

Comments

For n > 2, a(n) and a(n-1) share at least one prime factor.

Shows how many patterns can be created with 1-color thread while sewing on a button with buttonholes located on the vertices of a convex n-gon. - Ivan N. Ianakiev, Feb 09 2012

References

• Masha Gessen, Perfect Rigor, A Genius and the Mathematical Breakthrough of the Century, Houghton Mifflin Harcourt, 2009, page 38.

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..80

Crossrefs

Cf. A000217, A006125.

Programs

GAP

List([-1..15],n->2^(Binomial(2+n,n))-1); # Muniru A Asiru, Feb 21 2019

Maple

seq(2^(binomial(n+1, 2))-1, n=0..12); # Zerinvary Lajos, Jun 12 2007

Mathematica

FoldList[Times,2^Range[0,20]]-1 (* Harvey P. Dale, Sep 09 2015 *)
2^Accumulate[Range[0,20]]-1 (* Harvey P. Dale, Jun 03 2019 *)

Formula

a(n) = A006125(n+1) - 1. - Zerinvary Lajos, Jun 12 2007

Extensions

Corrected and extended by Harvey P. Dale, Sep 09 2015