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SequenceFold[f,{x1,…,xn},{a1,a2,…}]

gives the last element of SequenceFoldList[f,{x1,…,xn},{a1,a2,…}].

SequenceFold[f,{x1,…,xn},{a1,a2,…},k]

applies f to k arguments at each step, with the first n coming from the xi or previous results, and the last k-n coming from the ai.

Details
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Examples  
Basic Examples  
Scope  
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SequenceFold

SequenceFold[f,{x1,…,xn},{a1,a2,…}]

gives the last element of SequenceFoldList[f,{x1,…,xn},{a1,a2,…}].

SequenceFold[f,{x1,…,xn},{a1,a2,…},k]

applies f to k arguments at each step, with the first n coming from the xi or previous results, and the last k-n coming from the ai.

Details

  • In SequenceFold[f,{x1,…,xn},{a1,a2,…}], the function f is assumed to have n+1 arguments.
  • SequenceFold[f,{x},{a1,a2,…}] is equivalent to Fold[f,x,{a1,a2,…}].
  • SequenceFold[f,{x1,…,xn},{a1,a2,…}] is equivalent to SequenceFold[f,{x1,…,xn},{a1,a2,…},n+1].
  • In SequenceFold[f,{x1,…,xn},{a1,a2,…},k], the integer k must obey k≥n.

Examples

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Basic Examples  (2)

Successively apply a function f to a seed sequence x,y and the elements of a list:

Wolfram Language code: SequenceFold[f, {x, y}, {a, b}]

Successively apply a function f of 4 arguments to a seed sequence x,y and pairs of elements in a list:

Wolfram Language code: SequenceFold[f, {x, y}, {a, b, c}, 4]

Scope  (2)

Take one element from the list in the third argument in each iteration:

Wolfram Language code: SequenceFold[f, {x, y}, {a, b, c}]

Take several elements from the list in the third argument in each iteration:

Wolfram Language code: list = SequenceFold[f, {x, y}, {a, b, c, d}, 4]

Properties & Relations  (5)

SequenceFold[f,xlist,alist] returns the last element of SequenceFoldList[f,xlist,alist]:

Wolfram Language code: SequenceFold[Plus, {1, 1}, ConstantArray[0, 10]]
Wolfram Language code: SequenceFoldList[Plus, {1, 1}, ConstantArray[0, 10]]

Starting with a seed sequence of length 1 makes SequenceFold equivalent to Fold:

Wolfram Language code: SequenceFold[f, {x}, {a, b, c}]
Wolfram Language code: Fold[f, x, {a, b, c}]

An empty seed sequence makes SequenceFold apply the function to the last element of the final list:

Wolfram Language code: SequenceFold[f, {}, {a, b, c}]

If f has only one argument, then SequenceFold is equivalent to Nest:

Wolfram Language code: SequenceFold[f, {x}, {a, b, c, d}, 1]
Wolfram Language code: Nest[f, x, 5]

The number of arguments of the function cannot be smaller than the length of the seed sequence:

Wolfram Language code: SequenceFold[f, {x, y, z}, {a, b, c}, 2]

If they are equal, then the actual elements of the list in the third argument are not used:

Wolfram Language code: SequenceFold[f, {x, y, z}, {a, b, c}, 3]

Possible Issues  (1)

This case is not well defined, and hence it is left unevaluated:

Wolfram Language code: SequenceFold[f, {}, {}]
Wolfram Research (2015), SequenceFold, Wolfram Language function, https://reference.wolfram.com/language/ref/SequenceFold.html.

Text

Wolfram Research (2015), SequenceFold, Wolfram Language function, https://reference.wolfram.com/language/ref/SequenceFold.html.

CMS

Wolfram Language. 2015. "SequenceFold." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SequenceFold.html.

APA

Wolfram Language. (2015). SequenceFold. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SequenceFold.html

BibTeX

@misc{reference.wolfram_2026_sequencefold, author="Wolfram Research", title="{SequenceFold}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/SequenceFold.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_sequencefold, organization={Wolfram Research}, title={SequenceFold}, year={2015}, url={https://reference.wolfram.com/language/ref/SequenceFold.html}, note=[Accessed: 12-June-2026]}