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A157265 a(n) = 36*n^2 - 17*n + 2. 5
21, 112, 275, 510, 817, 1196, 1647, 2170, 2765, 3432, 4171, 4982, 5865, 6820, 7847, 8946, 10117, 11360, 12675, 14062, 15521, 17052, 18655, 20330, 22077, 23896, 25787, 27750, 29785, 31892, 34071, 36322, 38645, 41040, 43507, 46046, 48657, 51340 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (10368*n^2-4896*n+577)^2-(36*n^2-17*n+2)* (1728*n-408)^2=1 can be written as A157267(n)^2-a(n)* A157266(n)^2=1 (see also the second comment in A157267). - Vincenzo Librandi, Jan 27 2012
The continued fraction expansion of sqrt(a(n)) is [6n-2; {1, 1, 2, 1, 1, 12n-4}]. - Magus K. Chu, Sep 09 2022
LINKS
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 27 2012
G.f.: x*(21 + 49*x + 2*x^2)/(1-x)^3. - Vincenzo Librandi, Jan 27 2012
E.g.f.: (36*x^2 + 19*x + 2)*exp(x) - 2. - G. C. Greubel, Feb 04 2018
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {21, 112, 275}, 40] (* Vincenzo Librandi, Jan 27 2012 *)
PROG
(PARI) a(n)=36*n^2-17*n+2 \\ Charles R Greathouse IV, Jan 11 2012
(Magma) I:=[21, 112, 275]; [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 27 2012
CROSSREFS
Sequence in context: A182827 A364268 A255285 * A275916 A355510 A129135
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 26 2009
STATUS
approved

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Last modified April 23 11:04 EDT 2024. Contains 371905 sequences. (Running on oeis4.)