A120580 Hankel transform of sum{k=0..n, C(2k,k)}.

1, 0, -4, -8, 0, 32, 64, 0, -256, -512, 0, 2048, 4096, 0, -16384, -32768, 0, 131072, 262144, 0, -1048576, -2097152, 0, 8388608, 16777216, 0, -67108864, -134217728, 0, 536870912, 1073741824, 0, -4294967296, -8589934592, 0, 34359738368, 68719476736, 0, -274877906944, -549755813888, 0

Offset

0,3

Comments

Hankel transform of A006134.

Hankel transform of A098479. [Paul Barry, Sep 19 2008]

Hankel transform of A025565. [Paul Barry, Mar 26 2010]

Links

Table of n, a(n) for n=0..40.

Paul Barry, Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices, Journal of Integer Sequences, 19, 2016, #16.3.5.

Index entries for linear recurrences with constant coefficients, signature (2,-4).

Formula

G.f.: (1-2x)/(1-2x+4x^2).

a(n) = 2^n*(cos(Pi*n/3)-sin(Pi*n/3)/sqrt(3)).

Mathematica

LinearRecurrence[{2, -4}, {1, 0}, 50] (* Harvey P. Dale, Feb 13 2023 *)

Crossrefs

Cf. A104538.

Sequence in context: A244123 A280652 A104538 * A205508 A013328 A143462

Adjacent sequences: A120577 A120578 A120579 * A120581 A120582 A120583

Keyword

easy,sign

Author

Paul Barry, Jun 15 2006

Status

approved