A228108 Number of pairs (x, y) with 0 <= x, y <= n such that the distance between two points is a positive integer.

4, 18, 48, 108, 204, 342, 528, 780, 1100, 1494, 1968, 2576, 3292, 4122, 5104, 6240, 7524, 8962, 10560, 12348, 14324, 16494, 18864, 21600, 24572, 27786, 31248, 34996, 39012, 43362, 48000, 52968, 58244, 63834, 69840, 76308, 83132, 90318, 97872, 105972, 114468, 123378, 132704, 142500, 152892, 163742, 175056

Offset

1,1

Comments

Pairs ((0, 1), (0, 0)) and ((0, 0), (0, 1)) are considered equal since they have the same points. ((0, 0), (0, 0)) isn't counted the distance between the points included isn't a positive integer. The x's and y's of points in a pair may differ due to Pythagoras, for example ((0, 0), (3, 4)).

Links

David A. Corneth, Table of n, a(n) for n = 1..10560

Wikipedia, Pythagorean triple

Prog

(PARI) a(n)=my(tot=n*(n+1)^2); forstep(i=1, sqrt(ceil(sqrt(n))^2)*(1+sqrt(2))\1, 2, forstep(j=2, max(sqrt(ceil(sqrt(n+i^2))^2)\1, n\(2*i))*(1+sqrt(2))\1, 2, if(gcd(i, j)==1, for(k=1, n\max(2*i*j, abs(j^2-i^2)),
tot+=(n-2*i*j*k+1)*(n-abs(j^2-i^2)*k+1)*4)))); tot \\David A. Corneth

Crossrefs

Sequence in context: A163188 A114364 A045991 * A259451 A181860 A027271

Adjacent sequences: A228105 A228106 A228107 * A228109 A228110 A228111

Keyword

nonn

Author

David A. Corneth, Aug 10 2013

Status

approved