|
|
A199338
|
|
y-values in the solution to 15*x^2 - 14 = y^2.
|
|
2
|
|
|
1, 11, 19, 89, 151, 701, 1189, 5519, 9361, 43451, 73699, 342089, 580231, 2693261, 4568149, 21203999, 35964961, 166938731, 283151539, 1314305849, 2229247351, 10347508061, 17550827269, 81465758639, 138177370801, 641378561051, 1087868139139, 5049562729769
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
When are both n+1 and 15*n+1 perfect squares? This problem gives the equation 15*x^2-14=y^2.
|
|
LINKS
|
|
|
FORMULA
|
a(n+4) = 8*a(n+2) - a(n) with a(1)=1, a(2)=11, a(3)=19, a(4)=89.
G.f.: x*(1+x)*(1+10*x+x^2)/(1-8*x^2+x^4). - Bruno Berselli, Nov 08 2011
|
|
MATHEMATICA
|
LinearRecurrence[{0, 8, 0, -1}, {1, 11, 19, 89}, 50]
|
|
PROG
|
(Magma) m:=29; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+x)*(1+10*x+x^2)/(1-8*x^2+x^4))); // Bruno Berselli, Nov 08 2011
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|