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

0,3

Comments

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

Links

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

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

Mathematica

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

Prog

(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)

Crossrefs

Cf. A000217, A073587, A076127, A190405.

Sequence in context: A104344 A100288 A076094 * A003719 A363884 A181033

Adjacent sequences: A076128 A076129 A076130 * A076132 A076133 A076134

Keyword

easy,nonn,base

Author

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

Extensions

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

Formula corrected by Vaclav Kotesovec, Aug 11 2012

Status

approved