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A157440
a(n) = 121*n^2 - 204*n + 86.
3
3, 162, 563, 1206, 2091, 3218, 4587, 6198, 8051, 10146, 12483, 15062, 17883, 20946, 24251, 27798, 31587, 35618, 39891, 44406, 49163, 54162, 59403, 64886, 70611, 76578, 82787, 89238, 95931, 102866, 110043, 117462, 125123, 133026, 141171
OFFSET
1,1
COMMENTS
The identity (14641*n^2 - 24684*n + 10405)^2 - (121*n^2 - 204*n + 86)*(1331*n - 1122)^2 = 1 can be written as A157442(n)^2 - a(n)*A157441(n)^2 = 1. - Vincenzo Librandi, Jan 29 2012
The continued fraction expansion of sqrt(a(n)) is [11n-10; {1, 2, 1, 2, 11n-10, 2, 1, 2, 1, 22n-20}]. For n=1, this collapses to [1; {1, 2}]. - Magus K. Chu, Sep 13 2022
FORMULA
G.f.: x*(-3 - 153*x - 86*x^2)/(x-1)^3. - Vincenzo Librandi, Jan 29 2012
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 29 2012
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {3, 162, 563}, 50] (* Vincenzo Librandi, Jan 29 2012 *)
PROG
(PARI) a(n)=121*n^2-204*n+86 \\ Charles R Greathouse IV, Dec 28 2011
(Magma) I:=[3, 162, 563]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 29 2012
CROSSREFS
Sequence in context: A302950 A173128 A377253 * A157559 A157586 A341224
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 01 2009
STATUS
approved