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A300761 Number of non-equivalent ways (mod D_2) to select 4 points from n equidistant points on a straight line so that no selected point is equally distant from two other selected points. 2
0, 1, 3, 6, 15, 28, 53, 87, 140, 210, 310, 434, 600, 803, 1061, 1368, 1747, 2190, 2723, 3337, 4060, 4884, 5840, 6916, 8148, 9525, 11083, 12810, 14747, 16880, 19253, 21851, 24720, 27846, 31278, 34998, 39060, 43447, 48213, 53340, 58887, 64834, 71243, 78093, 85448 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,3

COMMENTS

The condition of the selection is also known as "no 3-term arithmetic progressions".

A reflection of a selection is not counted. If reflections are to be counted see A300760.

LINKS

Heinrich Ludwig, Table of n, a(n) for n = 4..1000

FORMULA

a(n) = (n^4 - 12*n^3 + 54*n^2 - 88*n)/48 + (n == 1 (mod 2))*(-4*n + 19)/16 + (n == 5 (mod 6))/3 + (n == 2 (mod 6))/3 + (n == 2 (mod 4))/2.

a(n) = (n^4 - 12*n^3 + 54*n^2 - 88*n)/48 + b(n) + c(n), where

  b(n) = 0              for n even

  b(n) = (-4*n + 19)/16 for n odd

  c(n) = 0              for n == 0,1,3,4,7,9 (mod 12)

  c(n) = 1/3            for n == 5,8,11      (mod 12)

  c(n) = 1/2            for n == 6,10        (mod 12)

  c(n) = 5/6            for n == 2           (mod 12).

From Colin Barker, Mar 15 2018: (Start)

G.f.: x^5*(1 + x + 4*x^3 + x^4 + 5*x^5) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)).

a(n) = 2*a(n-1) - a(n-3) - 2*a(n-5) + 2*a(n-6) + a(n-8) - 2*a(n-10) + a(n-11) for n>14.

(End)

CROSSREFS

Cf. A002623, A300760.

Sequence in context: A000740 A161625 A234848 * A069712 A076971 A103529

Adjacent sequences:  A300758 A300759 A300760 * A300762 A300763 A300764

KEYWORD

nonn,easy

AUTHOR

Heinrich Ludwig, Mar 15 2018

STATUS

approved

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Last modified July 13 07:30 EDT 2020. Contains 335676 sequences. (Running on oeis4.)