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A322556 The number of eigenvectors with eigenvalue 1 summed over all linear operators on the vector space GF(2)^n. 0
0, 1, 12, 448, 61440, 32505856, 67645734912, 558551906910208, 18374686479671623680, 2413129272746388704198656, 1266412660188944021221804081152, 2657157917355198038900481496478384128, 22295300680659888126120304278929453214597120 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Generally, for any prime power q, the total number of eigenvectors corresponding to any element lambda in the field GF(q) summed over all operators on GF(q)^n is equal to (q^n-1)*q^(n^2-n).

LINKS

Table of n, a(n) for n=0..12.

FORMULA

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

MATHEMATICA

Map[Total, Table[Table[(q^(n - k) - 1) Product[(q^n - q^i)^2/(q^k - q^i), {i, 0, k - 1}] /. q -> 2, {k, 0, n}], {n, 0, 11}]]

CROSSREFS

Cf. A286331.

Sequence in context: A291996 A192601 A092704 * A295413 A202799 A121348

Adjacent sequences:  A322553 A322554 A322555 * A322557 A322558 A322559

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Aug 28 2019

STATUS

approved

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Last modified September 16 23:53 EDT 2021. Contains 347477 sequences. (Running on oeis4.)