Various functions for working with the Banker's Sequence in a variety of languages
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The Banker's Sequence project status

This project contains various functions for working with the Banker's Sequence. The same concepts are implemented in various languages:

  • C
  • Java
  • JavaScript
  • Clojure


This work began with a simple observation of the bit string of successive numbers in the Banker's Sequence, as described in section 1 here. This lead to a search for a more efficient and non-recursive algorithm, which developed into a fast method of finding binomial coefficients.

The best description of this algorithm, and indeed problem, that I have found is on Eric Burnett's blog The Lowly Programmer. Eric gives a description of the reasoning behind the alorgithm and links to different implementations.


The C implementation has been designed for speed, not for a useable API. The functions use a fixed length bit string represented by an integer:

  • choose, an array backed calculation of binomial coefficients.
  • compute, translates from the natural numbers to the Banker's numbers.
  • inverse, translates from the Banker's numbers to the natural numbers.
  • next, produces the successive number from the given Banker's number.

The equivalent functions are also provided with arbitrary precision by using GMP.

The JavaScript implementation uses Strings of ones and zeros (e.g. "1000"). It is not considered fast or efficient.

The Java implementation is designed for power, speed and ease of use (although it is lacking a pom file). Binomial coefficients are calculated from a DAG that represents Pascal's Triangle, to which the algorithm leads itself to nicely.

The Clojure implementation is a complete rewrite of the Java implementation that takes advantage of Clojure's many features/libraries, including, persistant data structures, protocols, dynamic typing, automatic promotion to BigInts, clojure.test.check, etc.