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A232553 Maximal values of permanent on (0,1) square matrices of order n with row and column sums 3.

%I A232553 #44 Aug 09 2025 10:09:05
%S A232553 6,9,13,36,54,81,216,324,486,1296,1944,2916,7776,11664,17496,46656,
%T A232553 69984,104976,279936,419904,629856,1679616,2519424,3779136,10077696,
%U A232553 15116544,22674816,60466176,90699264,136048896,362797056,544195584,816293376,2176782336,3265173504,4897760256
%N A232553 Maximal values of permanent on (0,1) square matrices of order n with row and column sums 3.
%C A232553 a(n) is attained on the subset of symmetric matrices with the main diagonal all 1's.
%H A232553 Colin Barker, <a href="/A232553/b232553.txt">Table of n, a(n) for n = 3..1000</a>
%H A232553 D. Merriell, <a href="http://www.tandfonline.com/doi/abs/10.1080/03081088008817354">The maximum permanents in Lambda_n,k</a>, Linear and Multilinear Algebra, 1980, no.9, 81-91.
%H A232553 V. S. Shevelev, <a href="http://dx.doi.org/10.1007/BF01104103">Some problems of the theory of enumerating the permutations with restricted position</a>, Journal of Soviet Mathematics, 61 (4) (1992) 2272-2317
%H A232553 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,6).
%F A232553 a(n) = floor(6^((n-h)/3)*(3/2)^h), where h=0,1 or 2, such that n == h (mod 3).
%F A232553 From _Colin Barker_, May 27 2016: (Start)
%F A232553 a(n) = 6*a(n-3) for n>8. [Corrected by _Paolo Xausa_, Aug 08 2025]
%F A232553 G.f.: x^3*(6+9*x+13*x^2+3*x^5) / (1-6*x^3). (End)
%t A232553 LinearRecurrence[{0, 0, 6}, {6, 9, 13, 36, 54, 81}, 50] (* _Paolo Xausa_, Aug 08 2025 *)
%o A232553 (PARI) a(n) = h = n%3; floor(6^((n-h)/3)*(3/2)^h); \\ _Michel Marcus_, Nov 26 2013
%o A232553 (PARI) Vec(x^3*(6+9*x+13*x^2+3*x^5)/(1-6*x^3) + O(x^50)) \\ _Colin Barker_, May 27 2016
%Y A232553 Cf. A176211, A176212, A185177, A185178, A185179.
%K A232553 nonn,easy
%O A232553 3,1
%A A232553 _Vladimir Shevelev_, Nov 26 2013