A130496 Repetition of even numbers, with initial zeros, five times.

0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 14, 14, 14, 14, 14, 16, 16, 16, 16, 16, 18, 18, 18, 18, 18, 20, 20, 20, 20, 20, 22, 22, 22, 22, 22, 24, 24, 24, 24, 24, 26, 26, 26, 26, 26, 28, 28, 28, 28, 28, 30, 30, 30

Offset

0,6

Links

Table of n, a(n) for n=0..77.

Formula

a(n)= -2 + 2*Sum_{k=0..n} {[8*(sin(2*Pi*k/5))^2-5]^2-5}/20, with n>=0. a(n)= -2 + 2*Sum_{k=0..n} 1/50*{-9*[k mod 5]+[(k+1) mod 5]+[(k+2) mod 5]+[(k+3) mod 5]+11*[(k+4) mod 5]}, with n>=0.

a(n)=-2+2*Sum{k=0..n}{1-(k^4 mod 5)}, with n>=0 [From Paolo P. Lava, Feb 17 2010]

Maple

P:=proc(n) local i, j, k; for i from 0 by 1 to n do j:=-2+2*sum('(8*(sin(2*Pi*k/5))^2-5)^2-5', 'k'=0..i)/20; print(j); od; end: P(100);

Mathematica

Table[#, 5]&/@(2*Range[0, 15])//Flatten (* Harvey P. Dale, Sep 11 2016 *)

Crossrefs

Cf. A122461.

Sequence in context: A295101 A160675 A105674 * A187243 A001299 A001300

Adjacent sequences: A130493 A130494 A130495 * A130497 A130498 A130499

Keyword

easy,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, May 31 2007

Status

approved