|
Search: id:A118120
|
|
|
| A118120 |
|
Sequence allows us to find the solutions of the equation X^2+(X+17)^2=Y^2. |
|
+0
3
|
|
| 0, 7, 28, 51, 88, 207, 340, 555, 1248, 2023, 3276, 7315, 11832, 19135, 42676, 69003, 111568, 248755, 402220, 650307, 1450008, 2344351, 3790308, 8451307, 13663920, 22091575, 49257868, 79639203, 128759176, 287095935, 464171332, 750463515
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Consider all Pythagorean triples (X,X+17,Y) ordered by increasing Y; sequence gives X values.
|
|
REFERENCES
|
Mohamed Bouhamida(Algeria),E.Mail:bhmd95(AT)yahoo.fr
|
|
FORMULA
|
a(n)=6*a(n-3)-a(n-6)+34 with a(0)=0,a(1)=7,a(2)=28,a(3)=51,a(4)=88,a(5)=207.
|
|
MATHEMATICA
|
For the equation: X^2+(X+K)^2=Y^2 with K=2*m^2-1, m>=2 and K is not a power of a natural integer, the X values are given by the sequence defined by: a(n)=6*a(n-3)-a(n-6)+2K with a(0)=0, a(1)=2m+1, a(2)=6*m^2-10m+4, a(3)=3K, a(4)=6*m^2+10m+4, a(5)=40*m^2-58m+21. EX:K=7, 17, 31, 71, 97, 127, 161, 199, ... If K=199 than m=10.
|
|
CROSSREFS
|
Cf. A118554, A118611, A118630.
Sequence in context: A103253 A139607 A068206 this_sequence A078307 A045551 A024844
Adjacent sequences: A118117 A118118 A118119 this_sequence A118121 A118122 A118123
|
|
KEYWORD
|
nonn,uned
|
|
AUTHOR
|
Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 12 2006
|
|
|
Search completed in 0.002 seconds
|
