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A154358
a(n) = 1250*n^2 - 1800*n + 649.
5
649, 99, 2049, 6499, 13449, 22899, 34849, 49299, 66249, 85699, 107649, 132099, 159049, 188499, 220449, 254899, 291849, 331299, 373249, 417699, 464649, 514099, 566049, 620499, 677449, 736899, 798849, 863299, 930249
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 a(n)^2 - A154355(n)*A154360(n)^2 = 1. See also the third comment in A154357.
FORMULA
G.f.: (649 - 1848*x + 3699*x^2)/(1-x)^3. - R. J. Mathar, Jan 05 2011
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
E.g.f.: (649 - 550*x + 1250*x^2)*exp(x). - G. C. Greubel, Sep 14 2016
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {649, 99, 2049}, 50] (* Vincenzo Librandi, Feb 21 2012 *)
PROG
(PARI) for(n=0, 40, print1(1250*n^2 - 1800*n + 649", ")); \\ Vincenzo Librandi, Feb 21 2012
(Magma) [1250*n^2-1800*n+649: n in [0..40]]; // Bruno Berselli, Sep 15 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 08 2009
EXTENSIONS
Offset and one entry corrected by R. J. Mathar, Jan 05 2011
Librandi's comment rewritten by Bruno Berselli, Dec 13 2011
STATUS
approved