# Tom Johnson / Pascal's Triangle Modulo Seven ... and more

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here is a short program (based on JOHNSON's writing... pascal-code found in www and modified) to generate TOM JOHNSON's series of numbers for "pascal's triangle ...".

maybe interesting to play with the MODULO like JOHNSON did (mod 7)... try it!

greetings

andré

```;;; SUB
(defun pascal-next-row (a &key (johnson-modulo nil))
(loop :for q :in a
:and p = 0 :then q
:as s = (if (null johnson-modulo)
(list (+ p q))
(list (mod (+ p q) johnson-modulo)))
:nconc s :into a
:finally (rplacd s (list 1))
(return a)))

;;; MAIN
(defun pascal-triangle (n &key (johnson-modulo nil))
(loop :for a = (list 1) :then (pascal-next-row a :johnson-modulo johnson-modulo)
:repeat n
:collect a))

;;; => pascal-triangle
(pascal-triangle 7)
=> ((1) (1 1) (1 2 1) (1 3 3 1) (1 4 6 4 1) (1 5 10 10 5 1) (1 6 15 20 15 6 1))

;;; => pascal-triangle with MODULO like tom johnson in PASCAL'S TRIANGLE MODULO SEVEN
(pascal-triangle 21 :johnson-modulo 7)
=> ((1) (1 1) (1 2 1) (1 3 3 1) (1 4 6 4 1) (1 5 3 3 5 1) (1 6 1 6 1 6 1) (1 0 0 0 0 0 0 1) (1 1 0 0 0 0 0 1 1) (1 2 1 0 0 0 0 1 2 1) (1 3 3 1 0 0 0 1 3 3 1) (1 4 6 4 1 0 0 1 4 6 4 1) (1 5 3 3 5 1 0 1 5 3 3 5 1) (1 6 1 6 1 6 1 1 6 1 6 1 6 1) (1 0 0 0 0 0 0 2 0 0 0 0 0 0 1) (1 1 0 0 0 0 0 2 2 0 0 0 0 0 1 1) (1 2 1 0 0 0 0 2 4 2 0 0 0 0 1 2 1) (1 3 3 1 0 0 0 2 6 6 2 0 0 0 1 3 3 1) (1 4 6 4 1 0 0 2 1 5 1 2 0 0 1 4 6 4 1) (1 5 3 3 5 1 0 2 3 6 6 3 2 0 1 5 3 3 5 1) (1 6 1 6 1 6 1 2 5 2 5 2 5 2 1 6 1 6 1 6 1))

;;; look!!

(list-plot (flatten (pascal-triangle 50 :johnson-modulo 7))

(list-plot (flatten (pascal-triangle 50 :johnson-modulo 11))

(list-plot (flatten (pascal-triangle 80 :johnson-modulo 17))

(list-plot (flatten (pascal-triangle 50 :johnson-modulo 3))

;;; rnd-testing
(list-plot (flatten (pascal-triangle 80 :johnson-modulo (1+ (random 23))))

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listen to the processes...

```(make-omn :pitch (integer-to-pitch (pascal-triangle 50 :johnson-modulo (1+ (random 23))))
:length '(t)
:span :pitch)```

an example with parallel processes (chordized)..

```
(setf chordlist (loop
for i in (flatten (integer-to-pitch (pascal-triangle 20 :johnson-modulo (1+ (random 23)))))
for j in (flatten (integer-to-pitch (pascal-triangle 20 :johnson-modulo (1+ (random 23)))))
for k in (flatten (integer-to-pitch (pascal-triangle 20 :johnson-modulo (1+ (random 23)))))
append (chordize (list i j k))))

(make-omn :pitch chordlist
:length '(t)
:span :pitch)```

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