A126883 - OEIS

%I #25 Jul 09 2024 15:57:36

%S 0,1,7,63,1023,32767,2097151,268435455,68719476735,35184372088831,

%T 36028797018963967,73786976294838206463,302231454903657293676543,

%U 2475880078570760549798248447,40564819207303340847894502572031,1329227995784915872903807060280344575

%N 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.

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

%C 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

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

%H Muniru A Asiru, <a href="/A126883/b126883.txt">Table of n, a(n) for n = 0..80</a>

%F a(n) = A006125(n+1) - 1. - _Zerinvary Lajos_, Jun 12 2007

%p seq(2^(binomial(n+1, 2))-1, n=0..12); # _Zerinvary Lajos_, Jun 12 2007

%t FoldList[Times,2^Range[0,20]]-1 (* _Harvey P. Dale_, Sep 09 2015 *)

%t 2^Accumulate[Range[0,20]]-1 (* _Harvey P. Dale_, Jun 03 2019 *)

%o (GAP) List([-1..15],n->2^(Binomial(2+n,n))-1); # _Muniru A Asiru_, Feb 21 2019

%Y Cf. A000217, A006125.

%K nonn

%O 0,3

%A _Marco Matosic_, Dec 29 2006

%E Corrected and extended by _Harvey P. Dale_, Sep 09 2015