A076131 a(n) = 2^n*a(n-1) + 1, a(0) = 0.

0, 1, 5, 41, 657, 21025, 1345601, 172236929, 44092653825, 22575438758401, 23117249288602625, 47344126543058176001, 193921542320366288900097, 1588605274688440638669594625, 26027708820495411423962638336001, 852875962629993641540407732994080769

Offset: 0

Author

Kyle Hunter (hunterk(AT)raytheon.com), Oct 31 2002

Keywords

• easy
• nonn
• base

Comments

Base-2 expansion is same as base 10 expansion of A076127.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..80

Crossrefs

Cf. A000217, A073587, A076127, A190405.

Programs

Mathematica

a[0] = 0; a[n_] := 2^n a[n - 1] + 1; Table[ a[n], {n, 0, 13}]

PARI

a(n)=if(n<0,0,subst(Polrev(Vec(sum(k=1,n,x^(k*(k+1)/2)))),x,2))

PARI

a(n)=if(n<1,0,1+a(n-1)*2^n)

Formula

a(n) = floor(c*2^((n+1)*(n+2)/2)) where c = sum(k>=1, 1/2^A000217(k))=0.6416325... - Benoit Cloitre, Nov 01 2002

Extensions

Edited and extended by Robert G. Wilson v, Oct 31 2002

Formula corrected by Vaclav Kotesovec, Aug 11 2012