A248943 Sum of squares of diagonals of a parallelogram (but not rectangle or rhombus) with integer sides and diagonals and their GCD is 1.

130, 170, 250, 260, 290, 340, 370, 410, 442, 500, 530, 580, 610, 650, 650, 650, 730, 740, 754, 820, 850, 850, 850, 884, 890, 962, 970, 986, 1010, 1060, 1066, 1090, 1130, 1220, 1250, 1258, 1300, 1300, 1300, 1370, 1378, 1394, 1450, 1450, 1450, 1460, 1490, 1508, 1570, 1586, 1690, 1690, 1690, 1700, 1700, 1700, 1730

Offset

1,1

Comments

Alternate definition: Lists of P satisfying P = 2a^2 + 2b^2 = c^2 + d^2 (by parallelogram law) and a + b > max(c,d) (by triangle inequality) and a!=b (removes rhombus) and c!=d (removes rectangle) and gcd(a,b,c,d)=1.

Links

Table of n, a(n) for n=1..57.

Example

a...b...c...d...P=2a^2+2b^2=c^2+d^2
4...7...7...9...130
6...7...7...11..170
5...10..9...13..250
7...9...8...14..260
8...9...11..13..290
7...11..12..14..340
8...11..9...17..370
6...13..11..17..410
10..11..9...19..442
9...13..10..20..500

Mathematica

PMax=2000;
Do[Sqrt[P/2-a^2]//If[IntegerQ[#]&&GCD[a, #, c[[1]], c[[2]]]==1, P//Sow]&, {P, 2, PMax, 2}, {c, DeleteCases[PowersRepresentations[P, 2, 2], {x_, x_}]}, {a, (c[[2]]-c[[1]])/2+1, Sqrt[P]/2-1//Ceiling}]//Reap//Last//Last

Crossrefs

Sequence in context: A252369 A252362 A331629 * A248649 A050238 A115937

Adjacent sequences: A248940 A248941 A248942 * A248944 A248945 A248946

Keyword

nonn

Author

Albert Lau, Oct 17 2014

Status

approved