

A290562


a(n) = n  cos(n*Pi/2).


2



1, 1, 3, 3, 3, 5, 7, 7, 7, 9, 11, 11, 11, 13, 15, 15, 15, 17, 19, 19, 19, 21, 23, 23, 23, 25, 27, 27, 27, 29, 31, 31, 31, 33, 35, 35, 35, 37, 39, 39, 39, 41, 43, 43, 43, 45, 47, 47, 47, 49, 51, 51, 51, 53, 55, 55, 55, 57, 59, 59, 59, 61, 63, 63, 63, 65, 67
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OFFSET

0,3


COMMENTS

a(n) divides A289870(n).


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,2,2,1).


FORMULA

G.f.: (x^3  x^2 + 3 x  1)/((x  1)^2*(x^2 + 1)).
a(n) = n if n == 1 (mod 4), and a(n) = a(n4) + 4 otherwise, for n>4.
a(n) = a(n+20)  20.
a(n) = A290561(n).
a(n) + A290561(n) = 2*n.
a(n) * A290561(n) = n^2  cos(n*Pi/2)^2 = A085046(n) for n>0.
From Colin Barker, Aug 08 2017: (Start)
a(n) = n  (i)^n/2  i^n/2 where i=sqrt(1).
a(n) = 2*a(n1)  2*a(n2) + 2*a(n3)  a(n4) for n>3.
(End)


MATHEMATICA

a[n_] := n  Cos[n*Pi/2]; Table[a[n], {n, 0, 60}]


PROG

(PARI) a(n) = n  round(cos(n*Pi/2)); \\ Michel Marcus, Aug 06 2017
(PARI) Vec((x^3  x^2 + 3*x  1)/((x  1)^2*(x^2 + 1)) + O(x^100)) \\ Colin Barker, Aug 08 2017


CROSSREFS

Cf. A085046, A289870, A290561.
Sequence in context: A282243 A214748 A225225 * A307446 A122519 A141695
Adjacent sequences: A290559 A290560 A290561 * A290563 A290564 A290565


KEYWORD

sign,easy


AUTHOR

JeanFrançois Alcover and Paul Curtz, Aug 06 2017


STATUS

approved



