|
Search: id:A077925
|
|
|
| A077925 |
|
Expansion of 1/((1-x)*(1+2*x)). |
|
+0
21
|
|
| 1, -1, 3, -5, 11, -21, 43, -85, 171, -341, 683, -1365, 2731, -5461, 10923, -21845, 43691, -87381, 174763, -349525, 699051, -1398101, 2796203, -5592405, 11184811, -22369621, 44739243, -89478485, 178956971, -357913941, 715827883, -1431655765, 2863311531, -5726623061
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
a(n+1) is the reflection of a(n) through a(n-1) on the numberline. - Floor van Lamoen (fvlamoen(AT)hotmail.com), Aug 31 2004
If a zero is added as the (new) a(0) in front, the sequence represents the inverse binomial transform of A001045. Partial sums are in A077898. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 30 2008]
a(n) = A077953(2*n+3). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 07 2008]
|
|
FORMULA
|
G.f.: 1/(1+x-2*x^2).
a(n) = (1-(-2)^(n+1))/3. - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 17 2003
a(n)=sum{k=0..n, (-2)^k } - Paul Barry (pbarry(AT)wit.ie), May 26 2003
a(n+1)-a(n)=A122803(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 30 2008]
a(n)= Sum_{k, 0<=k<=n} A112555(n,k)*(-2)^k . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 11 2009]
a(n)= A082247(n+1)-1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 07 2009]
|
|
MAPLE
|
a:=n->sum ((-2)^j, j=0..n): seq(a(n), n=0..35); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 16 2008]
|
|
PROGRAM
|
(Other) sage: [gaussian_binomial(n, 1, -2) for n in xrange(1, 35)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
|
|
CROSSREFS
|
Cf. A001045 (unsigned version).
A014983, A014985, A014986 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 16 2008]
Sequence in context: A001045 A154917 A167167 this_sequence A084230 A077465 A146574
Adjacent sequences: A077922 A077923 A077924 this_sequence A077926 A077927 A077928
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2002
|
|
|
Search completed in 0.002 seconds
|
