A289383 Total number of nonzero vectors over all subspaces of an n-dimensional vector space over the field with two elements.

0, 1, 6, 35, 240, 2077, 23562, 358775, 7449060, 213188689, 8473977534, 470309723435, 36582636406680, 3998655357260293, 615328930033081458, 133485330929459963615, 40859530900982506959180, 17659495180812130332490681, 10781678259164073608877557286, 9301770545157096607562560360595

Offset

0,3

Comments

The q-analog of A001787.

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=1..n} A022166(n,k)*(2^k - 1).

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

a(n) = (2^n - 1)*A006116(n-1).

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[z eq[z]^2 /. q -> 2, {z, 0, nn}], z]

Crossrefs

Cf. A001787, A006116, A022166.

Sequence in context: A357828 A347002 A346945 * A249476 A346922 A355381

Adjacent sequences: A289380 A289381 A289382 * A289384 A289385 A289386

Keyword

nonn

Author

Geoffrey Critzer, Jul 04 2017

Status

approved