Integer Sequences nodes

Classic natural-number sequences composers reach for — Fibonacci, Lucas, Tribonacci, Primes, Triangular, Squares, Powers of 2, and Thue–Morse. Each node shares the same four knobs so they swap interchangeably:

Knob	Purpose
count	How many terms to generate.
offset	Skip the first N terms — which Fibonacci term to start from, which prime, etc.
modulo	Fold the sequence via x mod N. Set to 12 to keep Fibonacci pitches inside one octave; 0 disables.
scale	Multiply each term. Use 100 to convert step counts into semitone midicents for direct wiring into a Pitch Field.

All eight nodes output number[], which plugs straight into Pitch Field, Rhythm Tree, Arithmetic, Map Range, Slice, Repeat — anywhere a number list is accepted.

Node	First terms	Typical use
Fibonacci	0, 1, 1, 2, 3, 5, 8, 13, 21, 34…	Golden-ratio proportions — Bartók, Stockhausen, Xenakis. Fold mod 12 to land on a cyclic Pisano pitch pattern; scale by 100 for semitone midicents.
Lucas	2, 1, 3, 4, 7, 11, 18, 29, 47…	Fibonacci's sibling, starting 2, 1. Same golden-ratio limit; yields a different pitch palette when folded.
Tribonacci	0, 0, 1, 1, 2, 4, 7, 13, 24, 44…	Each term is the sum of the previous three. Grows faster than Fibonacci — good for rhythmic expansions.
Primes	2, 3, 5, 7, 11, 13, 17, 19, 23, 29…	Non-periodic, non-arithmetic. Classic source for Xenakis-style durations or irregular pitch intervals.
Triangular	0, 1, 3, 6, 10, 15, 21, 28, 36…	n(n+1)/2. Accumulating growth — sometimes used for compound meter sequences.
Squares	0, 1, 4, 9, 16, 25, 36, 49…	n2. Even more aggressive expansion. Mapped onto durations gives accelerating-retardation shapes.
Powers of 2	1, 2, 4, 8, 16, 32, 64, 128…	The metric ladder — whole, half, quarter, eighth… natural for nested subdivisions.
Thue–Morse	0, 1, 1, 0, 1, 0, 0, 1, 1, 0…	Parity of set-bits in n. Perfectly non-repeating binary sequence — drives on/off gates, "fair sharing" distributions, and morphological splits.

Studies that use these nodes