A154355 a(n) = 25*n^2 - 36*n + 13.

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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

Cf. A154354, A154358-A154361, A202141.

Essentially a duplicate of A007533.

Sequence in context: A040168 A176593 A031066 * A078421 A185808 A178548

Adjacent sequences: A154352 A154353 A154354 * A154356 A154357 A154358

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