A166514 Zig-zag function for first two columns of a matrix (take numbers in consecutive pairs).

0, 1, 1, 0, 2, 1, 3, 0, 4, 1, 5, 0, 6, 1, 7, 0, 8, 1, 9, 0, 10, 1, 11, 0, 12, 1, 13, 0, 14, 1, 15, 0, 16, 1, 17, 0, 18, 1, 19, 0, 20, 1, 21, 0, 22, 1, 23, 0, 24, 1, 25, 0, 26, 1, 27, 0, 28, 1, 29, 0, 30, 1, 31, 0, 32, 1, 33, 0, 34, 1, 35, 0, 36, 1, 37, 0, 38, 1, 39, 0, 40, 1, 41, 0, 42, 1, 43, 0

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: x(1+x-x^2+x^3)/((1+x)^2*(1-x)^2*(1+x^2)) = x(1+x-x^2+x^3)/(1-x^2-x^4+x^6);

a(n) = sin(Pi*n/2)/2 + (n-1)(-1)^n/4 + (n+1)/4.

Mathematica

CoefficientList[Series[(x + x^2 - x^3 + x^4)/((1 + x)^2*(1 - x)^2*(1 + x^2)), {x, 0, 50}], x] (* G. C. Greubel, May 15 2016 *)

Crossrefs

Sequence in context: A297109 A073312 A350941 * A246024 A278529 A160588

Adjacent sequences: A166511 A166512 A166513 * A166515 A166516 A166517

Keyword

easy,nonn

Author

Paul Barry, Oct 16 2009

Status

approved