(48G/50g) Binomial Transform, Difference Table

01172019, 09:56 PM
(This post was last modified: 09202019 02:04 PM by John Keith.)
Post: #1




(48G/50g) Binomial Transform, Difference Table
Difference tables and the binomial transform are powerful methods for analyzing integer sequences and their underlying logic. See also Conway and Guy, "The Book of Numbers", chapter 3.
Difference tables can be easily created using the \GDLIST (DeltaLIST) command on many HP calculators. Given a list of integers on level 1, the following program returns a difference table as a list of lists: Code:
A simple modification of the program above will return the inverse binomial transform of the list on level 1: Code:
Modifying the above program by inserting NEG after \GDLIST will produce the variation described by Thomas Klemm in this post. And finally another modification returns the binomial transform, the inverse of the function of the program above: Code:
Unlike \GDLIST, the two programs above do not shorten the list. If a list of integers is transformed by one program followed by the other, the original list will return unchanged. ...And one more useful variation, called "inverse summation" in this paper. Code:
This is the exact inverse of the cumulative or partial sum, and does not shorten the list. Edited 9/20/2019 to add NEWOB to binomial transform, inverse binomial transform, and inverse summation programs. This simple addition allows the programs to process much larger lists and makes the programs run somewhat faster. 

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Messages In This Thread 
(48G/50g) Binomial Transform, Difference Table  John Keith  01172019 09:56 PM
RE: (48G/50g) Binomial Transform, Difference Table  Thomas Klemm  01182019, 05:53 AM
RE: (48G/50g) Binomial Transform, Difference Table  John Keith  01182019, 08:01 PM
RE: (48G/50g) Binomial Transform, Difference Table  Thomas Klemm  01182019, 08:14 AM
RE: (48G/50g) Binomial Transform, Difference Table  John Keith  01182019, 07:39 PM
RE: (48G/50g) Binomial Transform, Difference Table  Thomas Klemm  01182019, 08:50 PM
RE: (48G/50g) Binomial Transform, Difference Table  John Keith  01182019, 09:44 PM
RE: (48G/50g) Binomial Transform, Difference Table  John Keith  05272019, 09:07 PM

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