A372217 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A372217

a(n) is the number of distinct triangles whose sides do not pass through a grid point and whose vertices are three points of an n X n grid.

0, 1, 3, 8, 14, 36, 48, 100, 146, 232, 294, 502, 595, 938, 1143, 1433, 1741, 2512, 2826, 3911, 4458, 5319, 6067, 7976, 8728, 10750, 12076, 14194, 15671, 19510, 20669, 25349, 28115, 31716, 34697, 39467, 41894, 49766, 54046, 59948, 63951, 74818, 78216, 90773, 97220

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..44.

Felix Huber, Illustration of the terms a(1) to a(6).

EXAMPLE

See the linked illustration for the terms a(1) = 1, a(2) = 3, a(3) = 8, a(4) = 14, a(5) = 36 and a(6) = 48.

MAPLE

S372217:=proc(n);

local s, x, u, v;

s:=0;

if n=1 then return 1 fi;

for x to n do

if gcd(x, n)=1 then

for u from x to n do

for v from 0 to n do

if gcd(u, v)=1 and gcd(u-x, n-v)=1 then

if u<n then s:=s+1;

elif v>=x then s:=s+1;

fi;

od;

fi;

od;

return s;

end proc;

A372217:=proc(n)

local i, a;

a:=0;

for i from 0 to n do

a:=a+S372217(i);

od;

return a;

end proc;

seq(A372217(n), n=0..44);

CROSSREFS

Cf. A115004, A141224, A141255, A320540, A320541, A320544, A372218.

Sequence in context: A168155 A005735 A208436 * A297015 A135872 A242245

Adjacent sequences: A372214 A372215 A372216 * A372218 A372219 A372220

KEYWORD

nonn

AUTHOR

Felix Huber, Apr 28 2024

STATUS

approved