A176211 - OEIS

%I #28 Jan 06 2021 12:43:12

%S 6,9,13,20,31,36,49,54,78,78,81,117,120,125,169,180,186,201,216,260,

%T 279,294,324,324,400,403,441,468,468,486,523,620,637,702,702,720,729,

%U 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

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

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

%C 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.

%C 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).

%H V. S. Shevelev, <a href="http://dx.doi.org/10.1007/BF01104103">Some problems of the theory of enumerating the permutations with restricted position</a>, Journal of Soviet Mathematics, 61 (4) (1992) 2272-2317.

%o (PARI) f(n) = fibonacci(n+1) + fibonacci(n-1) + 2; \\ A000211

%o 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));}

%o lista(14) \\ _Michel Marcus_, Jan 06 2021

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

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Apr 12 2010