A007533 a(n) = (5n+1)^2 + 4n+1. (Formerly M2162)

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

Also, numbers of the form (3k+1)^2 + (4k+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) = 25n^2 + 14n + 2.

G.f.: (2 + 35*x + 13*x^2)/(1-x)^3. (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

Sequence in context: A073186 A103335 A047936 * A088565 A090195 A287335

Adjacent sequences: A007530 A007531 A007532 * A007534 A007535 A007536

Keyword

nonn,easy

Author

N. J. A. Sloane, Robert G. Wilson v

Status

approved