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A122461 Repetitions of even numbers four times. 3
0, 0, 0, 0, 2, 2, 2, 2, 4, 4, 4, 4, 6, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 10, 12, 12, 12, 12, 14, 14, 14, 14, 16, 16, 16, 16, 18, 18, 18, 18, 20, 20, 20, 20, 22, 22, 22, 22, 24, 24, 24, 24, 26, 26, 26, 26, 28, 28, 28, 28, 30, 30, 30, 30, 32, 32, 32, 32, 34, 34, 34, 34, 36, 36, 36, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Number of roots of P(x) = 1 + x + x^2 + … + x^n in the right half-plane. - Michel Lagneau, Oct 30 2012

LINKS

Table of n, a(n) for n=0..75.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

FORMULA

a(n) = (Sum_{k=0..n} (k+1)*cos((n-k)*Pi/2))+1/4*(2*cos(n*Pi/2)+1+(-1)^n)-2. - Paolo P. Lava, May 15 2007

a(n) = 2*A002265(n) = 2*A180969(2,n). [Adriano Caroli, Nov 25 2010, corrected by R. J. Mathar, Nov 26 2010]

G.f.: 2*x^4/(1-x-x^4+x^5). [Bruno Berselli, Oct 31 2012]

a(n) = (-3+(-1)^n+2*i^((n-1)*n)+2*n)/4, where i=sqrt(-1). [Bruno Berselli, Oct 31 2012]

a(n) = 2 * floor(n/4). - Wesley Ivan Hurt, Dec 06 2013

a(n) = (2*n-3+2*cos(n*Pi/2)+cos(n*Pi)+2*sin(n*Pi/2))/4. - Wesley Ivan Hurt, Oct 02 2017

MAPLE

with(numtheory): for n from 1 to 70 do:it:=0:y:=[fsolve(sum('x^i ', 'i'=0..n-1), x, complex)] : for m from 1 to nops(y) do : if Re(y[m]) > 0 then it:=it+1:else fi:od: printf(`%d, `, it):od: # Michel Lagneau, Oct 31 2012

A122461:=n->2*floor(n/4); seq(A122461(n), n=0..100); # Wesley Ivan Hurt, Dec 06 2013

MATHEMATICA

Table[2 Floor[n/4], {n, 0, 100}] (* Wesley Ivan Hurt, Dec 06 2013 *)

CROSSREFS

Cf. A002265, A092533, A180969.

Sequence in context: A072376 A131883 A113452 * A092533 A092532 A073504

Adjacent sequences:  A122458 A122459 A122460 * A122462 A122463 A122464

KEYWORD

nonn,easy

AUTHOR

Paolo P. Lava and Giorgio Balzarotti, Oct 20 2006

STATUS

approved

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Last modified July 20 05:56 EDT 2019. Contains 325168 sequences. (Running on oeis4.)