|
| |
| |
|
|
|
1, 6, 26, 106, 426, 1706, 6826, 27306, 109226, 436906, 1747626, 6990506, 27962026, 111848106, 447392426, 1789569706, 7158278826, 28633115306, 114532461226, 458129844906, 1832519379626, 7330077518506
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Let Zb[n](x) = polynomial in x whose coefficients are the corresponding digits of index n in base b. Then Z2[(5*4^k-2)/3](1/tau) = 1 - Marc LeBrun, Mar 01 2001
a(n)=number of derangements of [2n+2] with runs consisting of consecutive integers. E.g. a(1)=6 because the derangements of {1,2,3,4} with runs consisting of consecutive integers are 4|123, 34|12, 4|3|12, 4|3|2|1, 234|1 and 34|2|1 (the bars delimit the runs). - Emeric Deutsch, May 26 2003
|
|
|
REFERENCES
|
J. Brillhart and P. Morton, A case study in mathematical research: the Golay-Rudin-Shapiro sequence, Amer. Math. Monthly, 103 (1996) 854-869.
Clifford A. Pickover, A Passion for Mathematics, John Wiley & Sons, Inc., 2005, at pp. 104 and 311 (for "Mr. Zanti's ants").
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
|
|
|
FORMULA
|
a(0)=1, a(n) = 4*a(n-1) + 2; a(n) = a(n-1)+ 5*{4^(n-1)}; - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 27 2001
G.f.:x*(1+x)/(1-4*x)/(1-x) . [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 11 2009]
|
|
|
MATHEMATICA
|
NestList[4#+2&, 1, 25] (* From Harvey P. Dale, Jul 23 2011 *)
|
|
|
PROG
|
(MAGMA) [(5*4^n-2)/3: n in [0..25]]; // Vincenzo Librandi, Jul 24 2011
|
|
|
CROSSREFS
|
A column of A119726.
Sequence in context: A196860 A037545 A027996 * A079675 A113991 A145374
Adjacent sequences: A020986 A020987 A020988 * A020990 A020991 A020992
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
STATUS
|
approved
|
| |
|
|
