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, 12153, 12699
Offset: 0
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).
Programs
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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 *) -
PARI
a(n)=3*(2*n^2+1) \\ Charles R Greathouse IV, Jun 17 2017
Formula
From Harvey P. Dale, Dec 29 2011: (Start)
a(0)=3, a(1)=9, a(2)=27, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: -3*(3*x^2+1)/(x-1)^3. (End)
From Elmo R. Oliveira, Feb 18 2025: (Start)
E.g.f.: 3*exp(x)*(1 + 2*x + 2*x^2).
a(n) = 3*A058331(n). (End)
Extensions
More terms from Robert G. Wilson v and Mark Hudson (mrmarkhudson(AT)hotmail.com), Aug 26 2004
Comments