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A110594
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a(1) = 4, a(2) = 12, for n>1: a(n) = 3*4^(n-1).
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5
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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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.
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FORMULA
| a(n) = A002001(n), n>1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 18 1008
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."
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CROSSREFS
| Cf. A000302, A007090, A081604, A110591, A110593.
Sequence in context: A056632 A149385 A092898 * A151483 A192622 A111930
Adjacent sequences: A110591 A110592 A110593 * A110595 A110596 A110597
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 29 2005
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EXTENSIONS
| Definition corrected by R. J. Mathar, Aug 18 2008
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