A097803 a(n) = 3*(2*n^2 + 1).

3, 9, 27, 57, 99, 153, 219, 297, 387, 489, 603, 729, 867, 1017, 1179, 1353, 1539, 1737, 1947, 2169, 2403, 2649, 2907, 3177, 3459, 3753, 4059, 4377, 4707, 5049, 5403, 5769, 6147, 6537, 6939, 7353, 7779, 8217, 8667, 9129, 9603, 10089, 10587, 11097, 11619

Offset

0,1

Comments

a(n) is also the number of Arnoux-Rauzy factors of length (n+1) over a 3-letter alphabet. - Genevieve Paquin (genevieve.paquin(AT)univ-savoie.fr), Nov 07 2008

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

F. Mignosi and L. Q. Zamboni, On the number of Arnoux-Rauzy words, Acta arith., 101 (2002), no. 2, 121-129. [From Genevieve Paquin (genevieve.paquin(AT)univ-savoie.fr), Nov 07 2008]

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(0)=3, a(1)=9, a(2)=27, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Dec 29 2011

G.f.: -((3*(3*x^2+1))/(x-1)^3). - Harvey P. Dale, Dec 29 2011

Mathematica

Table[ 3(2*n^2 + 1), {n, 0, 44}] (* Robert G. Wilson v, Aug 26 2004 *)
3(2Range[0, 50]^2+1) (* or *) LinearRecurrence[{3, -3, 1}, {3, 9, 27}, 50] (* Harvey P. Dale, Dec 29 2011 *)

Prog

(PARI) a(n)=3*(2*n^2+1) \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A097802.

Sequence in context: A093546 A015955 A357008 * A227097 A201202 A260938

Adjacent sequences: A097800 A097801 A097802 * A097804 A097805 A097806

Keyword

nonn,easy

Author

George E. Antoniou, Aug 25 2004

Extensions

More terms from Robert G. Wilson v and Mark Hudson (mrmarkhudson(AT)hotmail.com), Aug 26 2004

Status

approved