TOPICS
Search

Boustrophedon Transform

The boustrophedon ("ox-plowing") transform b of a sequence a is given by

b_n=sum_(k=0)^(n)(n; k)a_kE_(n-k)
(1)
a_n=sum_(k=0)^(n)(-1)^(n-k)(n; k)b_kE_(n-k)
(2)

for n>=0, where E_n is a secant number or tangent number defined by

sum_(n=0)^inftyE_n(x^n)/(n!)=secx+tanx.
(3)

The exponential generating functions of a and b are related by

B(x)=(secx+tanx)A(x),
(4)

where the exponential generating function is defined by

A(x)=sum_(n=0)^inftyA_n(x^n)/(n!).
(5)

See also

Alternating Permutation, Entringer Number, Secant Number, Seidel-Entringer-Arnold Triangle, Tangent Number

Explore with Wolfram|Alpha

References

Millar, J.; Sloane, N. J. A.; and Young, N. E. "A New Operation on Sequences: The Boustrophedon Transform." J. Combin. Th. Ser. A 76, 44-54, 1996.

Referenced on Wolfram|Alpha

Boustrophedon Transform

Cite this as:

Weisstein, Eric W. "Boustrophedon Transform." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BoustrophedonTransform.html

Subject classifications