|
| |
| |
|
|
|
0, 4, 20, 84, 340, 1364, 5460, 21844, 87380, 349524, 1398100, 5592404, 22369620, 89478484, 357913940, 1431655764, 5726623060, 22906492244, 91625968980, 366503875924, 1466015503700, 5864062014804, 23456248059220, 93824992236884, 375299968947540, 1501199875790164
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| a(n) is the number of steps which are made when generating all n-step random walks that begin in a given point P on a two-dimensional square lattice. To make one step means to move along one edge on the lattice. - Pawel P. Mazur (Pawel.Mazur(AT)pwr.wroc.pl), Mar 10 2005
Conjectured to be the number of integers from 0 to (10^n)-1 that lack 0, 1, 2, 3, 4 and 5 as a digit . - Alexandre Wajnberg (alexandre.wajnberg(AT)ulb.ac.be), Apr 25 2005
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..170
|
|
|
FORMULA
| a(n) = Sum_{i = 1 to n} 4^i. - Adam McDougall (mcdougal(AT)stolaf.edu), Sep 29 2004
a(n) = 4a(n-1) + 4 - Alexandre Wajnberg (alexandre.wajnberg(AT)ulb.ac.be), Apr 25 2005
a(n)=4^n+a(n-1) (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
|
|
|
EXAMPLE
| For n=1, a(1)=4+0=4; n=2, a(2)=4^2+4=20; n=3, a(3)=4^3+20=84 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
|
|
|
MATHEMATICA
| Table[4*(4^n-1)/3, {n, 0, 100}] (* From Vladimir Joseph Stephan Orlovsky, Jan 30 2012 *)
|
|
|
PROG
| (MAGMA) [(4/3)*(4^n-1): n in [0..40] ]; // Vincenzo Librandi, Apr 28 2011
|
|
|
CROSSREFS
| a(n) = 2 * A020988(n) = A002450(n+1)-1 = 4 * A002450(n).
Sequence in context: A167682 A155721 A084240 * A110154 A158608 A196953
Adjacent sequences: A080671 A080672 A080673 * A080675 A080676 A080677
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mar 02 2003
|
| |
|
|
