A166445 Hankel transform of A025276.

1, 0, -1, 1, 3, 0, -3, 1, 5, 0, -5, 1, 7, 0, -7, 1, 9, 0, -9, 1, 11, 0, -11, 1, 13, 0, -13, 1, 15, 0, -15, 1, 17, 0, -17, 1, 19, 0, -19, 1, 21, 0, -21, 1, 23, 0, -23, 1, 25, 0, -25, 1, 27, 0, -27, 1, 29, 0, -29, 1, 31, 0, -31, 1, 33, 0, -33, 1, 35, 0, -35, 1

Offset

0,5

Links

Felix Fröhlich, Table of n, a(n) for n = 0..10000

Han Wang and Zhi-Wei Sun, Evaluations of three determinants, arXiv:2206.12317 [math.NT], 2022.

Index entries for linear recurrences with constant coefficients, signature (1,-2,2,-1,1).

Formula

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

a(n) = (1/2)*(1 + cos((n+1)*Pi/2) + (n+1)*sin((n+1)*Pi/2)). - Harvey P. Dale, Nov 21 2014; corrected by Bernard Schott, Jun 27 2022

For n >= 0: a(4n) = 2n+1; a(4n+1) = 0; a(4n+2) = -a(4n) = -2n-1; a(4n+3) = 1. - Bernard Schott, Jun 27 2022

Mathematica

LinearRecurrence[{1, -2, 2, -1, 1}, {1, 0, -1, 1, 3}, 80] (* Harvey P. Dale, Nov 21 2014 *)

Prog

(PARI) Vec((1-x+x^2+x^4)/((1-x)*(1+x^2)^2) + O(x^80)) \\ Felix Fröhlich, Jun 28 2022

Crossrefs

Cf. A025276.

Sequence in context: A318505 A237595 A322575 * A298082 A085919 A352613

Adjacent sequences: A166442 A166443 A166444 * A166446 A166447 A166448

Keyword

easy,sign

Author

Paul Barry, Oct 13 2009

Extensions

More terms from Harvey P. Dale, Nov 21 2014

Status

approved