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

3,1

Comments

a(n) attains on subset of symmetric matrices with the main diagonal of 1's.

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).

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>5.

G.f.: x^3*(6+9*x+13*x^2+3*x^5) / (1-6*x^3).

(End)

Prog

(PARI) a(n) = h = n%3; floor(6^((n-h)/3)*(3/2)^h); \\ Michel Marcus, Nov 26 2013
(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

Crossrefs

Cf. A176211, A176212, A185177, A185178, A185179.

Sequence in context: A315974 A176211 A176212 * A155705 A267369 A177891

Adjacent sequences: A232550 A232551 A232552 * A232554 A232555 A232556

Keyword

nonn,easy

Author

Vladimir Shevelev, Nov 26 2013

Status

approved