A163823 Number of initial segments of signature sequences of length n.

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

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: A328596 A275692 A334267 * A015929 A331994 A043723

Adjacent sequences: A163820 A163821 A163822 * A163824 A163825 A163826

Keyword

nonn

Author

Franklin T. Adams-Watters, Aug 04 2009

Status

approved