|
|
A114336
|
|
Pythagorean triples of nearly isosceles triangle.
|
|
1
|
|
|
3, 4, 5, 20, 21, 29, 119, 120, 169, 696, 697, 985, 4059, 4060, 5741, 23660, 23661, 33461, 137903, 137904, 195025, 803760, 803761, 1136689, 4684659, 4684660, 6625109, 27304196, 27304197, 38613965, 159140519, 159140520, 225058681
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Pythagorean triples of exact isosceles triangles do not exist because 2a^2 = c^2 has no integer solution. a^2 + (a+1)^2 = c^2 are nearly isosceles triangles and give a recursive series.
|
|
LINKS
|
|
|
FORMULA
|
a^2 + (a+1)^2 = c^2, a(n) = 3a(n-1) + 2c(n-1) + 1, c(n) = 4a(n-1) + 3c(n-1) + 2.
|
|
EXAMPLE
|
119^2 + 120^2 = 169^2.
|
|
PROG
|
a(1):= 3 c(1):= 5 read m C m is infinite but limited by integer overflow of c(n) for n:=2 until m step 1 a(n):= 3*a(n-1) + 2*c(n-1) + 1 c(n):= 4*a(n-1) + 3*c(n-1) + 2 print a(n), a(n)+1, c(n) next n end
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn,tabf
|
|
AUTHOR
|
Heinrich Baldauf (heinbald25(AT)web.de), Feb 07 2006
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|