login
A166514
Zig-zag function for first two columns of a matrix (take numbers in consecutive pairs).
3
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
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 + (-1)^n)/4.
E.g.f.: (1/2)*(sin(x) + (1 + x)*sinh(x)). - G. C. Greubel, Aug 03 2024
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 *)
PROG
(Magma)
A166514:= func< n | ((n mod 2)*(1-(-1)^Floor((n+1)/2)) +((n+1) mod 2)*n)/2 >;
[A166514(n): n in [0..100]]; // G. C. Greubel, Aug 03 2024
(SageMath)
def A166514(n): return ((n%2)*(1+(-1)^((n-1)//2)) +((n+1)%2)*n)/2
[A166514(n) for n in range(101)] # G. C. Greubel, Aug 03 2024
CROSSREFS
Sequence in context: A297109 A073312 A350941 * A246024 A278529 A160588
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 16 2009
STATUS
approved