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A305737 Number of subsets S of vectors in GF(2)^n such that span(S) = GF(2)^n. 0
1, 2, 8, 184, 62464, 4293001088, 18446743803209556992, 340282366920938461120638132973980614656, 1157920892373161954235709850086879077664979811008012562545622603268018, 24546816 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Asymptotic to A001146(n) = 2^(2^n).

REFERENCES

R. P. Stanley, Enumerative Combinatorics Vol 1, Cambridge, 1997, page 127.

LINKS

Table of n, a(n) for n=0..9.

FORMULA

a(n) = Sum_{k=0..n} A022166(n,k)*(-1)^(n-k)*2^binomial(n-k,2)*(2^(2^k)-1).

MATHEMATICA

Table[Sum[QBinomial[n, k, q] (-1)^(n - k) q^Binomial[n - k, 2] (2^(q^k) - 1) /. q -> 2, {k, 0, n}], {n, 0, 8}]

CROSSREFS

Cf. A001146, A022166.

Sequence in context: A181234 A156526 A009505 * A028368 A056990 A234637

Adjacent sequences:  A305734 A305735 A305736 * A305738 A305739 A305740

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Jun 22 2018

STATUS

approved

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Last modified February 18 21:20 EST 2020. Contains 332028 sequences. (Running on oeis4.)