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A110594 a(1) = 4, a(2) = 12, for n>1: a(n) = 3*(4^n). +0
3
4, 12, 48, 192, 768, 3072, 12288, 49152, 196608, 786432, 3145728, 12582912, 50331648, 201326592, 805306368, 3221225472, 12884901888, 51539607552, 206158430208, 824633720832, 3298534883328, 13194139533312, 52776558133248 (list; graph; listen)
OFFSET

1,1

COMMENT

Since A110591 = "string-length of base 4 representation of n", we have A110591 = A110594 # 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.

FORMULA

a(1) = 4, a(2) = 12, for n>2: a(n+1) = 4*a(n). For n>1, cumulative sum of a(n) = A000302(n) = powers of 4. a(n) = the number of occurrences of the integer n in A110591 = "string-length of base 4 representation of n" = the number of occurrences of the integer n in "string-length of A007090."

CROSSREFS

Cf. A000302, A007090, A081604, A110591, A110593.

Sequence in context: A019309 A056632 A092898 this_sequence A111930 A013935 A104708

Adjacent sequences: A110591 A110592 A110593 this_sequence A110595 A110596 A110597

KEYWORD

easy,nonn

AUTHOR

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

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.


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