A289537 - OEIS

A289537

Triangle read by rows: T(n,k) is the number of k-dimensional subspaces of an n-dimensional vector space over F_2 that do not contain a given nonzero vector, n>=0, 0<=k<=n.

%I #19 Jul 16 2017 02:46:52

%S 1,1,0,1,2,0,1,6,4,0,1,14,28,8,0,1,30,140,120,16,0,1,62,620,1240,496,

%T 32,0,1,126,2604,11160,10416,2016,64,0,1,254,10668,94488,188976,85344,

%U 8128,128,0,1,510,43180,777240,3212592,3108960,690880,32640,256,0

%N Triangle read by rows: T(n,k) is the number of k-dimensional subspaces of an n-dimensional vector space over F_2 that do not contain a given nonzero vector, n>=0, 0<=k<=n.

%F T(n,k) = 2^k * A022166(n-1,k).

%e Triangle begins:

%e 1;

%e 1, 0;

%e 1, 2, 0;

%e 1, 6, 4, 0;

%e 1, 14, 28, 8, 0;

%e 1, 30, 140, 120, 16, 0;

%e 1, 62, 620, 1240, 496, 32, 0;

%t Table[Table[Product[q^n - q^i, {i, 1, k}]/Product[q^k - q^i, {i, 0, k - 1}] /. q -> 2, {k, 0, n}], {n, 0, 9}] // Grid

%Y Cf. A022166, A182176, A289538, A289539, A289541, A289542.

%K nonn,tabl

%O 0,5

%A _Geoffrey Critzer_, Jul 07 2017