Make a sequence for this?

Question

I've been exploring a family of functions and noticed a pattern in the continuity of their highest-order derivatives. Here's a list of the pattern I noticed:

n: {0, 0, 1, 1, 2, 2, 3, 3, 4, 4, ...} (so I'm just getting pairs that keep increasing)
k: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...}

These values are corresponding.

I'd like to make a sequence that generalizes this pattern, but can't think of any. Any ideas?

Anon E. Moose アナンイムース · Accepted Answer

n = ⌊(ℕ-1)/2⌋ = ⌈(ℕ-1)/2⌉ - (ℕ mod 2)
k = ℕ

Where ℕ refers to the Natural numbers = {1, 2, 3, ...}
⌊…⌋ is the floor function (Rounddown).
⌈…⌉ is the ceiling function (Roundup).

Just replace ℕ with k if you want to use Σ notation.

Make a sequence for this?

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