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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 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
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
Sequence in context: A107551 A202056 A229155 * A252538 A185666 A114047
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

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Last modified July 15 07:59 EDT 2024. Contains 374324 sequences. (Running on oeis4.)