A179510 Number of equally-spaced triples (x,y,z) of preceding terms with x+y=z

0, 0, 0, 1, 1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 9, 10, 10, 11, 12, 13, 13, 14, 15, 16, 17, 17, 18, 18, 19, 19, 20, 21, 22, 22, 23, 23, 24, 24, 25, 26, 26, 27, 28, 29, 30, 31, 31, 32, 32, 33, 34, 34, 35, 36, 36, 37, 38, 39, 39, 40, 41, 41, 42, 42, 43, 43, 44, 44, 45, 45, 46, 47, 47, 48, 49, 49, 50, 50, 51, 52, 53, 53, 54, 55, 56, 56, 57, 57, 58, 59, 60, 60, 61, 62, 62, 63, 64, 64, 65

Offset

0,6

Comments

a(n) is the number of 3-element subsets (i,j,k) of {0,...,n-1} such that k-j=j-i>0 and a(i)+a(j)=a(k). An induction argument can show simultaneously that a(n)-a(n-1) is always 0 or 1 and that the only case where three values of a(n) are equal is a(0)=a(1)=a(2)=0. Numerical evidence suggests that a(n) is asymptotic to 2n/3.

Links

Table of n, a(n) for n=0..100.

Example

For n=9, just the triples (0,1,2),(2,3,4),(3,4,5),(4,5,6),(4,6,8) satisfy the stated conditions, so a(9) = 5

Crossrefs

A178976 has a somewhat similar definition

Sequence in context: A204330 A225553 A039733 * A005374 A206767 A071991

Adjacent sequences: A179507 A179508 A179509 * A179511 A179512 A179513

Keyword

nonn,easy

Author

Alex Abercrombie, Jan 08 2011

Status

approved