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A176211
Numbers of the form Product_{m_i >= 3} A000211(m_i), possibly repeated, in natural order.
6
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
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
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Apr 12 2010
STATUS
approved