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A129756 Repetitions of odd numbers four times. 8
1, 1, 1, 1, 3, 3, 3, 3, 5, 5, 5, 5, 7, 7, 7, 7, 9, 9, 9, 9, 11, 11, 11, 11, 13, 13, 13, 13, 15, 15, 15, 15, 17, 17, 17, 17, 19, 19, 19, 19, 21, 21, 21, 21, 23, 23, 23, 23, 25, 25, 25, 25, 27, 27, 27, 27, 29, 29, 29, 29, 31, 31, 31, 31, 33, 33, 33, 33, 35, 35, 35, 35, 37, 37, 37, 37 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Conjecture: number of roots of  P(x) = x^n - x^(n-1) - x^(n-2) - ... - x - 1 in the right half-plane. - Michel Lagneau, Apr 09 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = (Sum_{k=0..n} (k+1)*cos((n-k)*Pi/2)) + (1/4)*(2*cos(n*Pi/2) + 1 + (-1)^n) - 1, with n >= 0.

a(n) = 1 + 2*floor(n/4) = 1 + 2*A002265(n). - R. J. Mathar, Jun 10 2007

G.f.: (1+x^4)/((-1+x)^2*(1+x)*(x^2+1)). - R. J. Mathar, Nov 18 2007

a(n) = -1 + Sum_{k=0..n} ((1/12)*(-5*(k mod 4)+((k+1) mod 4)+((k+2) mod 4)+7*((k+3) mod 4))). - Paolo P. Lava, Aug 21 2009

a(n) = n - A083219(n). - Michel Lagneau, Apr 09 2013

a(n) = (2*n+1+2*cos(n*Pi/2)+cos(n*Pi)+2*sin(n*Pi/2))/4. - Wesley Ivan Hurt, Oct 02 2017

MATHEMATICA

Table[1 + 2 Floor[n/4], {n, 0, 100}] (* Bruno Berselli, Jul 26 2014 *)

CoefficientList[Series[(1 + x^4)/(-1 + x)^2/(1 + x)/(x^2 + 1), {x, 0, 100}], x] (* Vincenzo Librandi, Jul 26 2014 *)

PROG

(MAGMA) [1+2*Floor(n/4): n in [0..100]]; // Bruno Berselli, Jul 26 2014

(MAGMA) I:=[1, 1, 1, 1, 3, 3, 3, 3, 5]; [n le 9 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..100]]; // Vincenzo Librandi, Jul 25 2014

CROSSREFS

Sequence in context: A190268 A111756 A130821 * A156724 A196186 A075753

Adjacent sequences:  A129753 A129754 A129755 * A129757 A129758 A129759

KEYWORD

nonn,easy

AUTHOR

Paolo P. Lava and Giorgio Balzarotti, May 15 2007

STATUS

approved

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Last modified March 25 03:50 EDT 2019. Contains 321450 sequences. (Running on oeis4.)