SequenceFoldList

SequenceFoldList[f, {x1, ..., xn}, {a1, a2, ...}] gives {x1, ..., xn, f[x1, ..., xn, a1], f[x2, ..., xn, f[x1, ..., xn, a1], a2], ...}.

• SequenceFoldList[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.

Examples

Basic sequence folding:

SequenceFoldList[Plus, {1, 2}, {3, 4, 5}]

With custom function:

SequenceFoldList[#1 + #2 + #3 &, {0, 1}, {1, 1, 1, 1}]

Fibonacci-like sequence:

SequenceFoldList[#1 + #2 &, {1, 1}, {0, 0, 0, 0, 0}]

Please visit the official Wolfram Language Reference for more details.