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A274462 Place n equally-spaced points around a circle, labeled 0,1,2,...,n-1. For each i = 0..n-1 such that 4i != i mod n, draw an (undirected) chord from i to (4i mod n). Then a(n) is the total number of distinct chords. 3
0, 0, 1, 0, 3, 2, 3, 6, 7, 6, 7, 10, 9, 12, 13, 6, 15, 16, 15, 18, 17, 18, 21, 22, 21, 22, 25, 24, 27, 28, 21, 30, 31, 30, 33, 32, 33, 36, 37, 36, 37, 40, 39, 42, 43, 36, 45, 46, 45, 48, 47, 48, 51, 52, 51, 52, 55, 54, 57, 58, 51 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..60.

Kival Ngaokrajang, Illustration of initial terms

FORMULA

We argue as in A273724. There are n-1 choices for i.

For nontrivial chords we need i != 4i mod n, which means 3i != 0 mod n, and so when n == 0 mod 3 we must subtract 2 from n-1.

A chord occurs twice (but must be counted only once) when j==4i mod n and i==4j mod n, thus when 15i==0 mod n. If n==+/- 5 mod 15 then subtract another 2, if n==0 mod 15 subtract 6.

Putting the pieces together, we obtain the g.f.

8 + x^2/(1-x)^2 - 2/(1-x^3) - 2(x^5+x^10)/(1-x^15) - 6/(1-x^15),

which can be rewritten as

x^2*(9*x^14-7*x^13+x^12+3*x^11-x^10+3*x^9+x^8-x^7+x^6+3*x^5+x^4-x^3+3*x^2-x+1)/((1-x)*(1-x^15)).

MAPLE

M:=4; # M is the multiplier (2 for A117571, 3 for A273724, 4 for the present sequence)

ans:=[0, 0];

for n from 2 to 100 do

h:=Array(0..n-1, 0..n-1, 0); ct:=0;

for i from 1 to n-1 do j := (M*i mod n);

if i<j then if h[i, j]=0 then ct:=ct+1; h[i, j]:=1; fi;

elif i>j then if h[j, i]=0 then ct:=ct+1; h[j, i]:=1; fi;

fi;

od:

ans:=[op(ans), ct];

od:

ans;  # N. J. A. Sloane, Jun 24 2016

CROSSREFS

If 4i in the definition is replaced by 2i we get A117571, and if 4i is replaced by 3i we get A273724.

Sequence in context: A208454 A187499 A187501 * A050062 A058533 A215413

Adjacent sequences:  A274459 A274460 A274461 * A274463 A274464 A274465

KEYWORD

nonn

AUTHOR

Brooke Logan, Jun 24 2016

STATUS

approved

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Last modified October 26 02:14 EDT 2021. Contains 348256 sequences. (Running on oeis4.)