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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
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).
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
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Aug 28 2019
STATUS
approved