A232553 Maximal values of permanent on (0,1) square matrices of order n with row and column sums 3.
6, 9, 13, 36, 54, 81, 216, 324, 486, 1296, 1944, 2916, 7776, 11664, 17496, 46656, 69984, 104976, 279936, 419904, 629856, 1679616, 2519424, 3779136, 10077696, 15116544, 22674816, 60466176, 90699264, 136048896, 362797056, 544195584, 816293376, 2176782336, 3265173504, 4897760256
Offset: 3
Links
- Colin Barker, Table of n, a(n) for n = 3..1000
- D. Merriell, The maximum permanents in Lambda_n,k, Linear and Multilinear Algebra, 1980, no.9, 81-91.
- V. S. Shevelev, Some problems of the theory of enumerating the permutations with restricted position, Journal of Soviet Mathematics, 61 (4) (1992) 2272-2317
- Index entries for linear recurrences with constant coefficients, signature (0,0,6).
Programs
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Mathematica
LinearRecurrence[{0, 0, 6}, {6, 9, 13, 36, 54, 81}, 50] (* Paolo Xausa, Aug 08 2025 *) -
PARI
a(n) = h = n%3; floor(6^((n-h)/3)*(3/2)^h); \\ Michel Marcus, Nov 26 2013
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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
Formula
a(n) = floor(6^((n-h)/3)*(3/2)^h), where h=0,1 or 2, such that n == h (mod 3).
From Colin Barker, May 27 2016: (Start)
a(n) = 6*a(n-3) for n>8. [Corrected by Paolo Xausa, Aug 08 2025]
G.f.: x^3*(6+9*x+13*x^2+3*x^5) / (1-6*x^3). (End)
Comments