1,1

Since A081604 = "string-length of ternary representation of n", we have A081604 = A110593 # n. This is in terms of the repetition convolution operator #, where (sequence A) # (sequence B) = the sequence consisting of A(n) copies of B(n). Over the set of positive infinite integer sequences, # gives a nonassociative noncommutative groupoid (magma) with a left identity (A000012) but no right identity, where the left identity is also a right nullifier, and idempotent. For any positive integer constant c, the sequence c*A000012 = (c,c,c,c,...) is also a right nullifier; for c = 1, this is A000012; for c = 3 this is A010701.

a(1) = 3, a(2) = 6, for n>2: a(n+1) = 3*a(n). For n>1, cumulative sum of a(n) = A000244 = powers of 3. a(n) = the number of occurrences of the integer n in A081604 = "string-length of ternary representation of n."

a(n) = A008776(n-1) for n>1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 24 2007

G.f.: 3x+6x^2/(1-3x). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 18 2007

Cf. A000244, A081604.

Sequence in context: A123891 A112572 A089325 this_sequence A049368 A102962 A076510

Adjacent sequences: A110590 A110591 A110592 this_sequence A110594 A110595 A110596

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Jul 29 2005