|
| |
|
|
A113311
|
|
Expansion of (1+x)^2/(1-x).
|
|
15
| |
|
|
1, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Row sums of A113310.
Let m=3. We observe that a(n)=sum{C(m,n-2*k),k=0..floor(n/2)). Then there is a link with A040000 and A115291: it is the same formula with respectively m=2 and m=4. We can generalize this result with the sequence whose G.f is given by (1+z)^(m-1)/(1-z). - Richard Choulet (richardchoulet(AT)yahoo.fr), Dec 08 2009
Also continued fraction expansion of (3+sqrt(5))/4. - Bruno Berselli, Sep 23 2011
Also decimal expansion of 121/900. - Vincenzo Librandi Sep 24 2011
|
|
|
LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1).
Vincenzo Librandi, Table of n, a(n) for n = 0..200
|
|
|
FORMULA
| a(n) = sum{k=0..n, sum{i=0..n-k, (-1)^i*C(i+k-2, i)}}.
|
|
|
MATHEMATICA
| CoefficientList[Series[(1+x)^2/(1-x), {x, 0, 110}], x] (* From Harvey P. Dale, Aug 19 2011 *)
|
|
|
CROSSREFS
| Cf. A040000, A115291, A171418, A171440, A171441, A171442, A171443.
Sequence in context: A007485 A018244 A090589 * A064042 A194882 A096343
Adjacent sequences: A113308 A113309 A113310 * A113312 A113313 A113314
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 25 2005
|
|
|
EXTENSIONS
| Spelling/notation corrections by Charles R Greathouse IV, Mar 18 2010
|
| |
|
|
