A176211 Numbers of the form Product_{m_i >= 3} A000211(m_i), possibly repeated, in natural order.

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

Author

Vladimir Shevelev, Apr 12 2010

Keywords

• nonn

Comments

Values represented by more than one set of indices are listed once per set; otherwise A176212 results.

Each term is a permanent of a quadratic symmetric (0,1) matrix with 1's on the main diagonal and exactly three 1's in each row and column.

For fixed Sum m_i=n with m_i >= 3, Product A000211(m_i) >= 6(4/3)^(n-3) and max(Product A000211(m_i)) = 6^((n-h)/3)*floor((3/2)^h), where h is the remainder of n (mod 3).

Links

• V. S. Shevelev, Some problems of the theory of enumerating the permutations with restricted position, Journal of Soviet Mathematics, 61 (4) (1992) 2272-2317.

Crossrefs

Cf. A176210, A036036, A036037, A080577, A138136, A000211.

Programs

PARI

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