

A113311


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


23



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
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OFFSET

0,2


COMMENTS

Row sums of A113310.
Let m=3. We observe that a(n)=sum{C(m,n2*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)^(m1)/(1z).  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..nk} (1)^i*C(i+k2, i).


MATHEMATICA

CoefficientList[Series[(1+x)^2/(1x), {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, A171440A171443.
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



