|
Search: id:A118673
|
|
|
| A118673 |
|
Positive solutions x to the equation x^2+(x+71)^2=y^2. |
|
+0
11
|
|
| 0, 13, 160, 213, 280, 1113, 1420, 1809, 6660, 8449, 10716, 38989, 49416, 62629, 227416, 288189, 365200, 1325649, 1679860, 2128713, 7726620, 9791113, 12407220, 45034213, 57066960, 72314749, 262478800, 332610789, 421481416, 1529838729
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Consider all Pythagorean triples (x,x+71,y) ordered by increasing y; sequence gives x values.
For the generic case x^2+(x+p)^2=y^2 with p=2*m^2-1 a prime number in A066436, m>=2 the associated value in A066049, the x values are given by the sequence defined by: a(n)=6*a(n-3)-a(n-6)+2p with a(0)=0, a(1)=2m+1, a(2)=6m^2-10m+4, a(3)=3p, a(4)=6m^2+10m+4, a(5)=40m^2-58m+21.
|
|
FORMULA
|
a(n)=6*a(n-3)-a(n-6)+142 with a(0)=0, a(1)=13, a(2)=160, a(3)=213, a(4)=280, a(5)=1113.
O.g.f.: x(13+147x+53x^2-11x^3-49x^4-11*x^5)/((1-x)(1-6x^3+x^6)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 10 2008
|
|
CROSSREFS
|
Cf. A076296 (p=7), A118120 (p=17), A118674 (p=31), A129836 (p=97), A129992 (p=127), A129993 (p=199), A129991 (p=241), A129999 (p=337), A130004 (p=449), A130005 (p=577), A130013 (p=647), A130014 (p=881), A130017 (p=967).
Sequence in context: A015470 A084328 A000830 this_sequence A133180 A090134 A087400
Adjacent sequences: A118670 A118671 A118672 this_sequence A118674 A118675 A118676
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 19 2006
|
|
EXTENSIONS
|
Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 10 2008
|
|
|
Search completed in 0.002 seconds
|
