

A128213


Expansion of (1x+2x^22x^3)/(1x+x^2)^2.


1



1, 1, 1, 1, 4, 4, 1, 7, 7, 1, 10, 10, 1, 13, 13, 1, 16, 16, 1, 19, 19, 1, 22, 22, 1, 25, 25, 1, 28, 28, 1, 31, 31, 1, 34, 34, 1, 37, 37, 1, 40, 40, 1, 43, 43, 1, 46, 46, 1, 49, 49, 1, 52, 52, 1, 55, 55, 1, 58, 58, 1, 61, 61, 1
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OFFSET

0,5


COMMENTS

a(n+1) is the Hankel transform of {1,0,1,3,9,28,90,297,1001,3432,11934,...}, cf. A000245.
Binomial transform of A128214.
a(n+2) is the Hankel transform of A014138.  Paul Barry, Mar 15 2008


LINKS

Table of n, a(n) for n=0..63.
Index entries for linear recurrences with constant coefficients, signature (2,3,2,1).


FORMULA

a(n) = cos(Pi*n/3) + (2n/sqrt(3)1/sqrt(3))*sin(Pi*n/3).
a(n) = y(n,n), where y(m+1,n) = y(m,n)  y(m1,n), with y(0,n)=1 and y(1,n)=n.  Benedict W. J. Irwin, Nov 05 2016


MATHEMATICA

Table[DifferenceRoot[Function[{y, m}, {y[1 + m] == y[m]  y[m  1], y[0] == 1, y[1] == n}]][n], {n, 0, 100}] (* Benedict W. J. Irwin, Nov 05 2016 *)


PROG

(PARI) Vec((1x+2*x^22*x^3)/(1x+x^2)^2 + O(x^100)) \\ Michel Marcus, May 31 2014


CROSSREFS

Sequence in context: A337191 A341863 A047213 * A171716 A211788 A318732
Adjacent sequences: A128210 A128211 A128212 * A128214 A128215 A128216


KEYWORD

easy,sign


AUTHOR

Paul Barry, Feb 19 2007


STATUS

approved



