A289542 Number of ordered pairs of nonzero vectors over the subspaces of GF(2)^n.

0, 1, 12, 119, 1290, 16957, 285264, 6343523, 190424310, 7826128009, 444658035228, 35162773747631, 3888419271339330, 603295404971492053, 131635270366023841896, 40458451431717420232187, 17536781855825299937977230, 10728658644626168469625854241

Offset: 0

Author

Geoffrey Critzer, Jul 15 2017

Keywords

• nonn

Crossrefs

Cf. A182176, A289537, A289538, A289539, A289541.

Programs

Mathematica

nn = 20; 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 (z + 2 z^2) /. q -> 2, {z, 0, nn}], z]

Formula

a(n)/[n]_q! is the coefficient of x^n in the expansion of (exp_q(x))^2*(x + 2 x^2) when q->2 and where exp_q(x) is the q-exponential function and [n]_q! is the q-factorial of n.