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A178976 Number of collinear triples in graph of preceding terms 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A130766 A227190 A284581

Adjacent sequences:  A178973 A178974 A178975 * A178977 A178978 A178979

KEYWORD

nonn,easy

AUTHOR

Alex Abercrombie, Jan 06 2011

STATUS

approved

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Last modified June 22 17:18 EDT 2021. Contains 345388 sequences. (Running on oeis4.)