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A099957 a(n) = Sum_{i=0..n-1} phi(2i+1). 6
1, 3, 7, 13, 19, 29, 41, 49, 65, 83, 95, 117, 137, 155, 183, 213, 233, 257, 293, 317, 357, 399, 423, 469, 511, 543, 595, 635, 671, 729, 789, 825, 873, 939, 983, 1053, 1125, 1165, 1225, 1303, 1357, 1439, 1503, 1559, 1647, 1719, 1779, 1851, 1947 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The n-th term is the number of notes of the (2n-1)-limit tonality diamond. This is a term from music theory and means the scale consisting of the rational numbers r, 1 <= r < 2, such that the odd part of both the numerator and the denominator of r, when reduced to lowest terms, is less than or equal to the fixed odd number 2n-1. - Gene Ward Smith, Mar 27 2006

(1/4)*Number of distinct angular positions under which an observer positioned at the center of a square of a square lattice can see the (2n) X (2n) points symmetrically surrounding his position.

(1/8)*number of distinct angular positions under which an observer positioned at a lattice point of a square lattice can see the (2n+1)X(2n+1) points symmetrically surrounding his position gives A002088.

(1/2)*number of distinct angular positions under which an observer positioned at the center of an edge of a square lattice can see the (2n)X(2n-1) points symmetrically surrounding his position gives A099958.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Wikipedia, Tonality diamond

FORMULA

a(n+1)-a(n)=phi(2n+1) (A037225).

CROSSREFS

Bisection of A274401.

Cf. A000010, A002088, A099958, A049687.

Sequence in context: A147614 A171747 A031215 * A086148 A262086 A205956

Adjacent sequences:  A099954 A099955 A099956 * A099958 A099959 A099960

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Nov 13 2004

STATUS

approved

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Last modified February 16 02:39 EST 2019. Contains 320140 sequences. (Running on oeis4.)