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

1,1

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

Table of n, a(n) for n=1..63.

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

Prog

(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

Crossrefs

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

Sequence in context: A315972 A315973 A315974 * A176212 A232553 A155705

Adjacent sequences: A176208 A176209 A176210 * A176212 A176213 A176214

Keyword

nonn

Author

Vladimir Shevelev, Apr 12 2010

Status

approved