[math-fun] Out of curiosity

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?