This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A056449 #63 Oct 28 2024 12:13:36
%S A056449 1,3,3,9,9,27,27,81,81,243,243,729,729,2187,2187,6561,6561,19683,
%T A056449 19683,59049,59049,177147,177147,531441,531441,1594323,1594323,
%U A056449 4782969,4782969,14348907,14348907,43046721,43046721,129140163,129140163,387420489,387420489,1162261467
%N A056449 a(n) = 3^floor((n+1)/2).
%C A056449 One followed by powers of 3 with positive exponent, repeated. - _Omar E. Pol_, Jul 27 2009
%C A056449 Number of achiral rows of n colors using up to three colors. E.g., for a(3) = 9, the rows are AAA, ABA, ACA, BAB, BBB, BCB, CAC, CBC, and CCC. - _Robert A. Russell_, Nov 07 2018
%D A056449 M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
%H A056449 Vincenzo Librandi, <a href="/A056449/b056449.txt">Table of n, a(n) for n = 0..2000</a>
%H A056449 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,3).
%F A056449 G.f.: (1 + 3*x) / (1 - 3*x^2). - _R. J. Mathar_, Jul 06 2011 [Adapted to offset 0 by _Robert A. Russell_, Nov 07 2018]
%F A056449 a(n) = k^ceiling(n/2), where k = 3 is the number of possible colors. - _Robert A. Russell_, Nov 07 2018
%F A056449 a(n) = C(3,0)*A000007(n) + C(3,1)*A057427(n) + C(3,2)*A056453(n) + C(3,3)*A056454(n). - _Robert A. Russell_, Nov 08 2018
%F A056449 E.g.f.: cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x). - _Stefano Spezia_, Dec 31 2022
%t A056449 Riffle[3^Range[0, 20], 3^Range[20]] (* _Harvey P. Dale_, Jan 21 2015 *)
%t A056449 Table[3^Ceiling[n/2], {n,0,40}] (* or *)
%t A056449 LinearRecurrence[{0, 3}, {1, 3}, 40] (* _Robert A. Russell_, Nov 07 2018 *)
%o A056449 (Magma) [3^Floor((n+1)/2): n in [0..40]]; // _Vincenzo Librandi_, Aug 16 2011
%o A056449 (PARI) a(n)=3^floor((n+1)/2); \\ _Joerg Arndt_, Apr 23 2013
%o A056449 (Python)
%o A056449 def A056449(n): return 3**(n+1>>1) # _Chai Wah Wu_, Oct 28 2024
%Y A056449 Column k=3 of A321391.
%Y A056449 Cf. A000007, A000244, A016116, A056391, A056453, A056454, A057427.
%Y A056449 Essentially the same as A108411 and A162436.
%Y A056449 Cf. A000244 (oriented), A032120 (unoriented), A032086(n>1) (chiral).
%K A056449 nonn,easy
%O A056449 0,2
%A A056449 _Marks R. Nester_
%E A056449 Edited by _N. J. A. Sloane_ at the suggestion of _Klaus Brockhaus_, Jul 03 2009
%E A056449 a(0)=1 prepended by _Robert A. Russell_, Nov 07 2018