Re: [math-fun] Out of curiosity

Stupid observation: replacing 3 by 1, you get 0,1,1,2,2,3,3,... On Tue, Dec 4, 2018 at 5:13 PM David Wilson <davidwwilson@comcast.net> wrote:

The triangular numbers can be defined by

a(0) = 0 a(1) = 1 a(2k) = 3a(k) + a(k - 1) a(2k+1) = 3a(k) + a(k + 1)

Out of curiosity, I replaced the 3 with 2, and

a(0) = 0 a(1) = 1 a(2k) = 2a(k) + a(k - 1) a(2k+1) = 2a(k) + a(k + 1)

seems to generate A174868.

BTW, the conjecture that A174868 = A007729 modulo offset, that shouldn't be too hard to prove, should it?

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