Problem 46034. Construct the Seidel-Entringer-Arnold triangle

Several problems in Cody ask us to construct part or all of triangles in which entries follow a pattern. Cody Problems 37, 1463, 44037, and 44904 involve Pascal's triangle, which consists of the binomial coefficients, and Cody Problem 1845 extends Pascal's triangle to a pyramid. Cody Problem 45460 involves the Bernoulli triangle, which consists of partial sums of the binomial coefficients.
This problem deals with the Seidel-Entringer-Arnold triangle (also called the Euler-Bernoulli triangle and the secant-tangent triangle). The first eight layers are
1
0 1
1 1 0
0 1 2 2
5 5 4 2 0
0 5 10 14 16 16
61 61 56 46 32 16 0
0 61 122 178 224 256 272 272
The name "secant-tangent triangle" arises because the sides contain the coefficients in the Taylor series for sec(x) and tan(x):
sec(x) = 1 + 1x^2/2! + 5x^4/4! + 61x^6/6! + ...
tan(x) = 1x + 2x^3/3! + 16x^5/5! + 272x^7/7! + ...
Construct the nth layer of this triangle.
Hint: Use the boustrophedon (or ox-plowing) rule.
Solve

Solution Stats

51.22% Correct | 48.78% Incorrect
Last Solution submitted on Apr 01, 2025

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers21

Suggested Problems

More from this Author314

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!