|
| |
|
|
A127976
|
|
Numbers of the form ((6*n + 10)/27)*2^(n-1) + ((-1)^(n-1))*(6*n + 5)/27.
|
|
10
| |
|
|
1, 1, 5, 9, 25, 53, 125, 273, 609, 1325, 2885, 6217, 13353, 28517, 60685, 128641, 271857, 572829, 1203925, 2524345, 5281721, 11029461, 22991005, 47846129, 99420545, 206297613, 427508325, 884842793, 1829337929, 3777980485
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), May 25 2009: (Start)
Equals A001045, [1, 1, 3, 5, 11, 21, 43, 85,...] convolved with A078008,
[1, 0, 2, 2, 6, 10, 22,...] (End)
|
|
|
REFERENCES
| Bosma W. 2001. Signed bits and fast exponentiation. J. Th. des Nombres de Bordeaux Vol.13, Fasc. 1
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Bosma W. Signed bits and fast exponentiation.
|
|
|
FORMULA
| a(n) = ((6*n + 10)/27)*2^(n - 1) + (-1)^(n - 1)*(6*n + 5)/27
a(n) = +2*a(n-1) +3*a(n-2) -4*a(n-3) -4*a(n-4); g.f.: x*(1-x)/((1+x)^2*(1-2*x)^2). [Joerg Arndt, May 27 2011]
|
|
|
MATHEMATICA
| Table[((6n + 10)/27)2^(n - 1) + ((-1)^(n - 1) )(6n + 5)/27, {n, 1, 100}] (*Artur Jasinski*)
|
|
|
PROG
| (MAGMA) [((6*n + 10)/27)*2^(n - 1) + ((-1)^(n - 1))*(6*n + 5)/27: n in [1..40]]; // Vincenzo Librandi, May 26 2011
|
|
|
CROSSREFS
| A001045, A078008 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 25 2009]
Sequence in context: A025624 A147496 A147383 * A147286 A137199 A147512
Adjacent sequences: A127973 A127974 A127975 * A127977 A127978 A127979
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Feb 09 2007
|
| |
|
|
