A113311 Expansion of (1+x)^2/(1-x).

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

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, 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

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (1).

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] (* Harvey P. Dale, Aug 19 2011 *)

Prog

(PARI) a(n)=if(n>1, 4, 2*n+1) \\ Charles R Greathouse IV, Jun 12 2015

Crossrefs

Cf. A040000, A115291, A171418, A171440-A171443.

Sequence in context: A007485 A280356 A018244 * A255176 A288177 A349992

Adjacent sequences: A113308 A113309 A113310 * A113312 A113313 A113314

Keyword

nonn,easy

Author

Paul Barry, Oct 25 2005

Extensions

Spelling/notation corrections by Charles R Greathouse IV, Mar 18 2010

Status

approved