|
%I #47 Sep 08 2022 08:45:01
%S 1,6,6,36,36,216,216,1296,1296,7776,7776,46656,46656,279936,279936,
%T 1679616,1679616,10077696,10077696,60466176,60466176,362797056,
%U 362797056,2176782336,2176782336,13060694016,13060694016,78364164096
%N a(n) = 6^floor((n+1)/2).
%C Number of achiral rows of length n using up to six different colors. For a(3) = 36, the rows are AAA, ABA, ACA, ADA, AEA, AFA, BAB, BBB, BCB, BDB, BEB, BFB, CAC, CBC, CCC, CDC, CEC, CFC, DAD, DBD, DCD, DDD, DED, DFD, EAE, EBE, ECE, EDE, EEE, EFE, FAF, FBF, FCF, FDF, FEF, and FFF. - _Robert A. Russell_, Nov 08 2018
%C Also: a(n) is the number of palindromes with n digits using a maximum of six different symbols. - _David A. Corneth_, Nov 09 2018
%D 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 Vincenzo Librandi, <a href="/A056452/b056452.txt">Table of n, a(n) for n = 0..2000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,6).
%F a(n) = 6^floor((n+1)/2).
%F a(n) = 6*a(n-2). - _Colin Barker_, May 06 2012
%F G.f.: (1+6*x) / (1-6*x^2). - _Colin Barker_, May 06 2012 [Adapted to offset 0 by _Robert A. Russell_, Nov 08 2018]
%F a(n) = C(6,0)*A000007(n) + C(6,1)*A057427(n) + C(6,2)*A056453(n) + C(6,3)*A056454(n) + C(6,4)*A056455(n) + C(6,5)*A056456(n) + C(6,6)*A056457(n). - _Robert A. Russell_, Nov 08 2018
%p A056452:=n->6^floor((n+1)/2);
%t Riffle[6^Range[0, 20], 6^Range[20]] (* _Harvey P. Dale_, Jun 18 2017 *)
%t Table[6^Ceiling[n/2], {n,0,40}] (* or *)
%t LinearRecurrence[{0, 6}, {1, 6}, 40] (* _Robert A. Russell_, Nov 08 2018 *)
%o (Magma) [6^Floor((n+1)/2): n in [0..40]]; // _Vincenzo Librandi_, Aug 16 2011
%Y Column k=6 of A321391.
%Y Cf. A016116.
%Y Cf. A000400 (oriented), A056308 (unoriented), A320524 (chiral).
%K nonn,easy
%O 0,2
%A _Marks R. Nester_
%E a(0)=1 prepended by _Robert A. Russell_, Nov 08 2018
%E Name corrected by _David A. Corneth_, Nov 08 2018
|
