A333797 Total number of saturated chains in the lattices L_n(2) of subspaces (ordered by inclusion) of the vector space GF(2)^n.

1, 3, 14, 114, 1777, 55461, 3496868, 444131448, 113253936439, 57872769803787, 59203843739029706, 121190268142727296926, 496274148044956457612893, 4064981546636275903297015089, 66596592678542112197488335080432, 2182170552297789390998576752287351492

Offset: 0

Author

Geoffrey Critzer, Apr 05 2020

Keywords

• nonn

Comments

These are the chains counted in A293844 that are saturated. A chain C in poset P is saturated if there is no z in P - C such that x < z < y for some x,y in C and such that C union {z} is a chain.

Crossrefs

Cf. A289545, A293844.

Programs

Mathematica

nn = 15; eq[z_] :=Sum[z^n/FunctionExpand[QFactorial[n, q]], {n, 0, nn}];
Table[FunctionExpand[QFactorial[n, q]] /. q -> 2, {n, 0, nn}] CoefficientList[Series[eq[z]^2/(1 - z) /. q -> 2, {z, 0, nn}], z]

Formula

a(n)/A005329(n) is the coefficient of x^n in eq(x)^2/(1 - x) where eq(x) is the q-exponential function.

a(n) ~ A299998 * 2^(n*(n+1)/2). - Vaclav Kotesovec, Apr 07 2020