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A154355
a(n) = 25*n^2 - 36*n + 13.
9
13, 2, 41, 130, 269, 458, 697, 986, 1325, 1714, 2153, 2642, 3181, 3770, 4409, 5098, 5837, 6626, 7465, 8354, 9293, 10282, 11321, 12410, 13549, 14738, 15977, 17266, 18605, 19994, 21433, 22922, 24461, 26050, 27689, 29378
OFFSET
0,1
COMMENTS
The identity (1250*n^2 - 1800*n + 649)^2 - (25*n^2 - 36*n + 13)*(250*n - 180)^2 = 1 can be written as A154358(n)^2 - a(n)*A154360(n)^2 = 1. See also the third comment in A154357.
Numbers of the form (3n-2)^2 + (4n-3)^2. - Bruno Berselli, Dec 12 2011
FORMULA
a(n) = A007533(n-1), n>0. - R. J. Mathar, Jan 14 2009
G.f.: (13 - 37*x + 74*x^2)/(1-x)^3. - R. J. Mathar, Jan 05 2011
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Feb 21 2012
E.g.f.: (13 - 11*x + 25*x^2)*exp(x). - G. C. Greubel, Sep 14 2016
MATHEMATICA
Table[25n^2-36n+13, {n, 0, 40}] (* Harvey P. Dale, Apr 02 2011 *)
LinearRecurrence[{3, -3, 1}, {13, 2, 41}, 50] (* Vincenzo Librandi, Feb 21 2012 *)
PROG
(PARI) for(n=0, 40, print1(25*n^2 - 36*n + 13", ")); \\ Vincenzo Librandi, Feb 21 2012
(Magma) [25*n^2-36*n+13: n in [0..40]]; // Bruno Berselli, Sep 15 2016
CROSSREFS
Essentially a duplicate of A007533.
Sequence in context: A040168 A176593 A031066 * A078421 A185808 A178548
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 07 2009
EXTENSIONS
Offset corrected from R. J. Mathar, Jan 05 2011
First comment rewritten by Bruno Berselli, Dec 12 2011
STATUS
approved