A185178
Number of distinct values of the permanent of an n X n (0,1)-matrix with exactly three 1's in each row and each column.
Original entry on oeis.org
1, 1, 2, 4, 8, 18, 32, 61, 109
Offset: 3
- V. I. Bolshakov, On spectrum of permanent on Lambda_n^k, Proc. of Seminar on Discrete Math. and Appl., Moscow State Univ. (1986), 65-73 (in Russian).
Cf.
A001501 (number of n X n (0,1)-matrix with exactly three 1's in each row and each column).
A176211
Numbers of the form Product_{m_i >= 3} A000211(m_i), possibly repeated, in natural order.
Original entry on oeis.org
6, 9, 13, 20, 31, 36, 49, 54, 78, 78, 81, 117, 120, 125, 169, 180, 186, 201, 216, 260, 279, 294, 324, 324, 400, 403, 441, 468, 468, 486, 523, 620, 637, 702, 702, 720, 729, 750, 845, 961, 980, 1014, 1014, 1053, 1080, 1116, 1125, 1206, 1296, 1366, 1519, 1521, 1560, 1560, 1620, 1625, 1674, 1764, 1809, 1944, 1944, 2197, 2209
Offset: 1
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f(n) = fibonacci(n+1) + fibonacci(n-1) + 2; \\ A000211
lista(nn) = {my(v = vector(nn, k, f(k+2))); my(vmax = vecmax(v)); my(w = vector(nn, k, [0, logint(vmax, v[k])])); my(list=List()); forvec(x = w, if (vecmax(x), my(y = prod(k=1, #v, v[k]^x[k])); if (y <= vmax, listput(list, y)););); Vec(vecsort(list));}
lista(14) \\ Michel Marcus, Jan 06 2021
A185179
Irregular triangle, read by rows, of the A185178(n) values of the permanent of an n X n (0,1)-matrix (n>=3) with exactly three 1's in each row and each column.
Original entry on oeis.org
6, 9, 12, 13, 17, 18, 20, 36, 24, 25, 26, 27, 30, 31, 32, 54, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 48, 49, 52, 72, 78, 81, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 66, 68, 70, 72, 78, 84, 102, 108, 117, 120, 216
Offset: 3
Triangle begins:
6
9
12, 13
17, 18, 20, 36
24, 25, 26, 27, 30, 31, 32, 54
33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 48, 49, 52, 72, 78, 81
42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 66, 68, 70, 72, 78, 84, 102, 108, 117, 120, 216
- V. I. Bolshakov, On spectrum of permanent on Lambda_n^k, Proc. of Seminar on Discrete Math. and Appl., Moscow State Univ. (1986), 65-73 (in Russian).
A185177
Different values of the permanent in (0,1) quadratic matrices with exactly 3 ones in each row and each column, in the increasing order.
Original entry on oeis.org
6, 9, 12, 13, 17, 18, 20, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42
Offset: 1
- V. I. Bolshakov, On spectrum of permanent on Lambda_n^k, Proc. of Seminar on Discrete Math. and Appl., Moscow State Univ. (1986), 65-73 (in Russian).
A232553
Maximal values of permanent on (0,1) square matrices of order n with row and column sums 3.
Original entry on oeis.org
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
- 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).
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LinearRecurrence[{0, 0, 6}, {6, 9, 13, 36, 54, 81}, 50] (* Paolo Xausa, Aug 08 2025 *)
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a(n) = h = n%3; floor(6^((n-h)/3)*(3/2)^h); \\ Michel Marcus, Nov 26 2013
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Vec(x^3*(6+9*x+13*x^2+3*x^5)/(1-6*x^3) + O(x^50)) \\ Colin Barker, May 27 2016
A232636
The second largest value of permanent of (0,1) square matrices of order n with row and column sums equal to 3.
Original entry on oeis.org
34012224, 53747712, 131010048, 204073344, 322486272, 786060288, 1224440064, 1934917632, 4716361728, 7346640384, 11609505792, 28298170368, 44079842304, 69657034752, 169789022208, 264479053824, 417942208512
Offset: 30
Showing 1-6 of 6 results.
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