OFFSET
0,1
COMMENTS
Also, numbers of the form (3*k + 1)^2 + (4*k + 1)^2. - Bruno Berselli, Dec 11 2011
The continued fraction expansion of sqrt(a(n)) is [5n+1; {2, 2, 10n+2}]. For n=0, this collapses to [1; {2}]. - Magus K. Chu, Aug 27 2022
REFERENCES
W. Sierpiński, Elementary Theory of Numbers. Państ. Wydaw. Nauk., Warsaw, 1964, p. 323.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
W. Sierpiński, Elementary Theory of Numbers, Warszawa 1964.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Bruno Berselli, Dec 11 2011: (Start)
a(n) = 25*n^2 + 14*n + 2.
G.f.: (2 + 35*x + 13*x^2)/(1-x)^3. (End)
From Elmo R. Oliveira, Oct 31 2024: (Start)
E.g.f.: (2 + 39*x + 25*x^2)*exp(x).
a(n) = A154355(n+1).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
MATHEMATICA
Table[25n^2+14n+2, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {2, 41, 130}, 40] (* Harvey P. Dale, Dec 18 2013 *)
PROG
(Magma) [(5*n+1)^2 + 4*n+1: n in [0..40]]; // Vincenzo Librandi, May 02 2011
(PARI) a(n)=25*n^2 + 14*n + 2 \\ Charles R Greathouse IV, May 02 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved