

A099957


a(n) = Sum_{i=0..n1} 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
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OFFSET

1,2


COMMENTS

The nth term is the number of notes of the (2n1)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 2n1.  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(2n1) 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



