

A168052


Hankel transform of a Motzkin variant.


2



1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 39, 39, 40, 41, 41, 42, 43
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OFFSET

0,3


COMMENTS

Hankel transform of A168051.


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,1)


FORMULA

G.f.: (1+x^2)/((1+x)^2*(1x+x^2)).
a(n) = cos(Pi*n/3)/3 + sqrt(3)*sin(Pi*n/3)/9 + 2*(n+1)*(1)^n/3.
a(n) = A010892(n)/3 + 2*(1)^n*(n+1)/3.  R. J. Mathar, Sep 30 2012


MATHEMATICA

LinearRecurrence[{1, 0, 1, 1}, {1, 1, 2, 3}, 100] (* G. C. Greubel, Jul 07 2016 *)
CoefficientList[Series[(1 + x^2) / ((1 + x)^2 (1  x + x^2)), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 08 2016 *)


PROG

(MAGMA) I:=[1, 1, 2, 3]; [n le 4 select I[n] else  Self(n1)Self(n3) Self(n4): n in [1..65]]; // Vincenzo Librandi, Jul 08 2016


CROSSREFS

Cf. A010892, A168051.
Sequence in context: A093878 A317686 A156689 * A131737 A004396 A066481
Adjacent sequences: A168049 A168050 A168051 * A168053 A168054 A168055


KEYWORD

easy,sign


AUTHOR

Paul Barry, Nov 17 2009


STATUS

approved



