|
| |
|
|
A077854
|
|
Expansion of 1/((1-x)*(1-2*x)*(1+x^2)).
|
|
6
| |
|
|
1, 3, 6, 12, 25, 51, 102, 204, 409, 819, 1638, 3276, 6553, 13107, 26214, 52428, 104857, 209715, 419430, 838860, 1677721, 3355443, 6710886, 13421772, 26843545, 53687091, 107374182, 214748364, 429496729, 858993459, 1717986918, 3435973836, 6871947673
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Partial sums of A007910. [From Mircea Merca, Dec 27 2010]
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,3,-2).
|
|
|
FORMULA
| a(n) = 3*a(n-1)-3*a(n-2)+3*a(n-3)-2*a(n-4), with initial values 1 3 6 12.
a(n) = (1/10)*(2^(n+4) + (-1)^floor(n/2) - 2*(-1)^floor((n+1)/2) - 5).
Row sums of A130306. - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 20 2007
a(n) = floor(2^(n+3)/5) [From Gary Deltefs (gdetlefs(AT)aol.com), Sep 06 2010]
a(n) = round((2^(n+4)-5)/10) = floor((2^(n+3)-1)/5) = ceil((2^(n+3)-4)/5) = round((2^(n+3)-2)/5); a(n)=a(n-4)+3*2^(n-1) , n>3 . [From Mircea Merca, Dec 27 2010]
|
|
|
MAPLE
| a := proc(n) option remember; if n=0 then RETURN(1); fi; if n=1 then RETURN(3); fi; if n=2 then RETURN(6); fi; if n=3 then RETURN(12); fi; 3*a(n-1)-3*a(n-2)+3*a(n-3)-2*a(n-4); end;
seq(iquo(2^n, 5), n=3..35); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 20 2008
|
|
|
PROG
| (MAGMA) [Round((2^(n+4)-5)/10): n in [0..40]]; // Vincenzo Librandi, Jun 25 2011
|
|
|
CROSSREFS
| Equals A007909(n+3) - [n congruent 2, 3 mod 4].
Cf. A130306.
Sequence in context: A088970 A068425 A136444 * A187260 A099445 A004067
Adjacent sequences: A077851 A077852 A077853 * A077855 A077856 A077857
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2002
|
| |
|
|
