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A163823 Number of initial segments of signature sequences of length n. 1
1, 2, 4, 6, 8, 12, 14, 16, 20, 24, 26, 32, 34, 36, 42, 46, 48, 54, 56, 60, 66, 70, 72, 80, 84, 86, 92, 98, 100, 110, 112, 114, 118, 122, 126, 136, 138, 140, 146, 154, 156, 166, 168, 172, 182, 186, 188, 196, 200, 204, 210, 216, 218, 228, 234, 238, 244, 248, 250, 262 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The initial segments of signature sequences correspond to ranges of theta from a1/b1 to a2/b2 (including 1/0 as infinity); a/b appears as a bound, splitting two previous segments, at n = (a+1)(b+1)/2.

LINKS

Table of n, a(n) for n=1..60.

Eric Weisstein's World of Mathematics, Signature Sequence

FORMULA

a(n) = 1 + sum( 2<=k<=n, A163822(k)).

EXAMPLE

For n = 6, the sequences and corresponding ranges for theta are:

1,1,1,1,1,1 0/1..1/5

1,1,1,1,1,2 1/5..1/4

1,1,1,1,2,1 1/4..1/3

1,1,1,2,1,2 1/3..1/2

1,1,2,1,2,1 1/2..2/3

1,1,2,1,2,3 2/3..1/1

1,2,1,3,2,1 1/1..3/2

1,2,1,3,2,4 3/2..2/1

1,2,3,1,4,2 2/1..3/1

1,2,3,4,1,5 3/1..4/1

1,2,3,4,5,1 4/1..5/1

1,2,3,4,5,6 5/1..1/0

CROSSREFS

Cf. A163822.

Sequence in context: A139363 A091065 A275692 * A015929 A043723 A006998

Adjacent sequences:  A163820 A163821 A163822 * A163824 A163825 A163826

KEYWORD

nonn

AUTHOR

Franklin T. Adams-Watters, Aug 04 2009

STATUS

approved

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Last modified June 16 10:03 EDT 2019. Contains 324152 sequences. (Running on oeis4.)