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A157620 781250n^2 - 1107500n + 392499. 3
66249, 1302499, 4101249, 8462499, 14386249, 21872499, 30921249, 41532499, 53706249, 67442499, 82741249, 99602499, 118026249, 138012499, 159561249, 182672499, 207346249, 233582499, 261381249, 290742499, 321666249, 354152499 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (781250*n^2-1107500*n+392499)^2-(625*n^2-886*n +314)*(31250*n-22150)^2=1 can be written as a(n)^2-A157618(n)*A157619(n)^2=1.
LINKS
Vincenzo Librandi, X^2-AY^2=1
FORMULA
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: x*(-66249-1103752*x-392499*x^2)/(x-1)^3.
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {66249, 1302499, 4101249}, 30]
PROG
(Magma) I:=[66249, 1302499, 4101249]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n) = 781250*n^2 - 1107500*n + 392499.
CROSSREFS
Sequence in context: A156424 A092376 A251333 * A174757 A164129 A043591
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 03 2009
STATUS
approved

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Last modified May 29 11:52 EDT 2024. Contains 372940 sequences. (Running on oeis4.)