k-bonacci numbers generalized into a square array.

[Joshua Weinstein]

Hello fellow SeqFans,

I was wondering about the possibility of creating a sequence based on the antidiagonals of a k-bonacci square array. Heres what I mean:

Lets define a k-bonacci sequence to be a sequence such that a(n) = a(n-1) + a(n-2) + ... + a(n-k), where a(0) = a(1) = ... a(k-2) = 0 and a(k-1) = 1. The first few examples of course would be A000045, A000073, and A000078.

Here's what the grid array might look like with k as rows and n as columns: A few things I was wondering: Should k-bonacci sequences only be defined for k>=2? (in which case I will delete the 0th and 1st rows.) Is the sequence of the antidiagonals of general interest? If so, does anyone know of a formula/code to generate the antidiagonals? Perhaps also the sum of the antidiagonals could be cool to explore. Also, apologies if any part of the definition seems vague or I made any mistakes/asked trivial questions. I hope theres enough context so you all know what I mean regardless. All the best, Joshua

[Joshua Weinstein]

Hi all,

Looks like the sequence is already in the OEIS https://oeis.org/A092921 and I should check Cfs more carefully. I didn't find this sequence in the database initially because my intuition about the first row was wrong, leading to my search not containing enough correct terms to find it.

Apologies,

Joshua