A289545 Number of flags in an n-dimensional vector space over GF(2).

1, 1, 4, 36, 696, 27808, 2257888, 369572160, 121459776768, 79991977040128, 105466641591287296, 278244130564826548224, 1468496684404408240109568, 15502543140842029367582248960, 327332729703063815298568073396224, 13823536566775628445052117519260598272

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..80

Geoffrey Critzer, Combinatorics of Vector Spaces over Finite Fields, Master's thesis, Emporia State University, 2018.

Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

Formula

a(n) = Sum A005329(n)/( A005329(n_1)*A005329(n_2)*...*A005329(n_k) ) where the sum is over all compositions of n = n_1 + n_2 + ... + n_k.

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

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[ 1/(1 - (eq[z] - 1)) /. q -> 2, {z, 0, nn}], z]

Crossrefs

Sequence in context: A029989 A163887 A156630 * A322782 A145565 A360903

Adjacent sequences: A289542 A289543 A289544 * A289546 A289547 A289548

Keyword

nonn

Author

Geoffrey Critzer, Jul 28 2017

Status

approved