# 96.20 Pascal's triangle: The hidden stor-e

@article{Brothers20129620PT, title={96.20 Pascal's triangle: The hidden stor-e}, author={Harlan J. Brothers}, journal={The Mathematical Gazette}, year={2012}, volume={96}, pages={145 - 148} }

shallow diagonal before that one. So the sum of any shallow diagonal (from the third onwards) is the sum of the two previous shallow diagonals, giving the inductive definition F" = Fn _ 1 + Fn _ 2 for Fibonacci numbers F", with F1 = I and F2 = 1, since these are the only numbers in the first two shallow diagonals. In the short-cut triangle, a similar relationship means that, after the third shallow diagonal, each element of any shallow diagonal is the sum of one element from each of the three…

## 3 Citations

A Surprising Link Between Integer Partitions and Euler’s Number e

- MathematicsAm. Math. Mon.
- 2019

Nathan Fine pioneered these types of sums, and one of his theorems is used to derive a general result that converges to any .

Pascal's Prism

- MathematicsThe Mathematical Gazette
- 2012

Pascal's triangle is well known for its numerous connections to probability theory [1], combinatorics, Euclidean geometry, fractal geometry, and many number sequences including the Fibonacci series…

The Asymptotic Behavior of N K

- Mathematics
- 2013

We determine the complete asymptotic expansion of n k=0 n k .

## References

SHOWING 1-9 OF 9 REFERENCES

Pascal's arithmetical triangle : the story of a mathematical idea

- Mathematics
- 2002

Contents: The Figurate Numbers Three Combinatorial Rules The Combinatorial Numbers in India The Combinatorial Numbers in the West The Binomial Numbers Pascal's Treatise on the Arithmetical Triangle…

Improving the Convergence of Newton's Series Approximation for e

- Art
- 2004

Harlan Brothers (hjb@thecountryschool.org) is Director of Technology at The Country School in Madison, Connecticut, where he teaches programming, fractal geometry, robotics, and jazz band. He is…

Pascal's legacy

- PhysicsEMBO reports
- 2004

The musings of a Belgian monk 300 years ago on the consequences of believing in God, or not, have influenced our Western life probably more than any other scientific or technological invention

Sebah, The constant e and its computation

- http://www.brotherstechnology.com/math!gourdon-and-sebah.html HARLAN 1. BROTHERS Brothers Technology. LLC, PO Box 1016,
- 2010

Pascal's legacy, EMBO reports

- Special Issue
- 2004

The Story of a Number

- 1994

Pascal's Triangle, from Math World -A Wolfram Web Resource

The constant e and its computation