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A157110 a(n) = 1681*n^2 - 2606*n + 1010. 3
85, 2522, 8321, 17482, 30005, 45890, 65137, 87746, 113717, 143050, 175745, 211802, 251221, 294002, 340145, 389650, 442517, 498746, 558337, 621290, 687605, 757282, 830321, 906722, 986485, 1069610, 1156097, 1245946, 1339157, 1435730, 1535665 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (5651522*n^2 - 8761372*n + 3395619)^2 - (1681*n^2 - 2606*n + 1010)*(137842*n - 106846)^2 = 1 can be written as A157112(n)^2 - a(n)*A157111(n)^2 = 1. - Vincenzo Librandi, Jan 25 2012
The continued fraction expansion of sqrt(a(n)) is [41n-32; {4, 1, 1, 4, 82n-64}]. - Magus K. Chu, Oct 03 2022
LINKS
Vincenzo Librandi, X^2-AY^2=1 [Broken link]
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 25 2012
G.f.: x*(-85 - 2267*x - 1010*x^2)/(x-1)^3. - Vincenzo Librandi, Jan 25 2012
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {85, 2522, 8321}, 40] (* Vincenzo Librandi, Jan 25 2012 *)
PROG
(Magma) I:=[85, 2522, 8321]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 25 2012
(PARI) for(n=1, 22, print1(1681*n^2 - 2606*n + 1010", ")); \\ Vincenzo Librandi, Jan 25 2012
CROSSREFS
Sequence in context: A221339 A262062 A220736 * A076463 A281162 A339198
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 23 2009
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)