OFFSET
1,1
COMMENTS
The identity (1250*n^2 + 100*n + 1)^2 - (25*n^2 + 2*n)*(250*n + 10)^2 = 1 can be written as A154375(n)^2 - a(n)*A154379(n)^2 = 1 (see also the second comment in A154375). - Vincenzo Librandi, Jan 30 2012
The continued fraction expansion of sqrt(4*a(n)) is [10n; {2, 1, 1, 5n-1, 1, 1, 2, 20n}]. - Magus K. Chu, Sep 27 2022
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: x*(27 + 23*x)/(1-x)^3.
E.g.f.: (25*x^2 + 27*x)*exp(x). - G. C. Greubel, Sep 15 2016
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {27, 104, 231}, 50]
PROG
(PARI) a(n)=25*n^2+2*n \\ Charles R Greathouse IV, Dec 23 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 08 2009
STATUS
approved