A178976 Number of collinear triples in graph of preceding terms

0, 0, 0, 1, 1, 1, 2, 4, 4, 4, 5, 5, 5, 6, 8, 11, 11, 12, 12, 12, 14, 14, 14, 16, 18, 20, 22, 24, 26, 29, 29, 29, 30, 31, 32, 35, 35, 35, 37, 38, 40, 43, 43, 45, 46, 50, 51, 52, 55, 55, 57, 57, 59, 61, 63, 65, 69, 69, 74, 74, 74, 76, 77, 78, 81, 82, 82, 86, 89, 91, 93, 96, 99, 100, 104, 105, 106, 107, 108, 112, 113, 115, 115, 117, 121, 122, 122, 124, 124, 125, 126, 131, 133, 134, 137, 139, 141, 146, 148, 150

Offset

0,7

Comments

a(n) is the number of 3-element subsets (i<j<k) of (0,...,n-1) such that both i,j,k and a(i),a(j),a(k) are arithmetic progressions (including the case a(i)=a(j)=a(k)). That is, k-j=j-i>0 and a(k)-a(j)=a(j)-a(i).

The sequence appears to grow faster than n but slower than n^(1+c) for any positive c.

Links

Table of n, a(n) for n=0..99.

Example

For n=7, the triples (0,1,2),(0,3,6),(2,4,6),(3,4,5) satisfy the stated conditions, so a(7)=4

Crossrefs

Sequence in context: A108421 A104058 A132345 * A352426 A372323 A130766

Adjacent sequences: A178973 A178974 A178975 * A178977 A178978 A178979

Keyword

nonn,easy

Author

Alex Abercrombie, Jan 06 2011

Status

approved