

A274462


Place n equallyspaced points around a circle, labeled 0,1,2,...,n1. For each i = 0..n1 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 n1 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 n1.
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/(1x)^2  2/(1x^3)  2(x^5+x^10)/(1x^15)  6/(1x^15),
which can be rewritten as
x^2*(9*x^147*x^13+x^12+3*x^11x^10+3*x^9+x^8x^7+x^6+3*x^5+x^4x^3+3*x^2x+1)/((1x)*(1x^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..n1, 0..n1, 0); ct:=0;
for i from 1 to n1 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



