(It’s interesting that the descriptions of this sequence in OEIS don’t mention anything trivially equivalent to what GSE has asked about here.)
Perhaps not trivially so, but this one from that page is exactly the one I worked out when I looked at the problem, and what I programmed to compute the table:
a(1)=1, else a(n) is sum of [ n/2 ] previous terms.
There’s an edge case at the very start that means that the OP’s sequence has an extra 1 at the beginning.
I was thinking of the material in the “Comment” section, which lists various examples of where the sequence arises, often (as here) of the form “a(n) = total number of objects of such-and-such a kind satisfying such-and-such conditions”. It’s true that one of the recurrence relations listed there also arises very straightforwardly from GSE’s definition of the sequence, but that’s not the same thing.
Perhaps not trivially so, but this one from that page is exactly the one I worked out when I looked at the problem, and what I programmed to compute the table:
There’s an edge case at the very start that means that the OP’s sequence has an extra 1 at the beginning.
I was thinking of the material in the “Comment” section, which lists various examples of where the sequence arises, often (as here) of the form “a(n) = total number of objects of such-and-such a kind satisfying such-and-such conditions”. It’s true that one of the recurrence relations listed there also arises very straightforwardly from GSE’s definition of the sequence, but that’s not the same thing.