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A086098 Sum of rank(M) over all n X n matrices over GF(2). 3
1, 21, 1141, 208965, 139889701, 354550756581, 3464730268306021, 131934922593867875685, 19707939574875773323508581, 11599530748705611712884878698341, 26983642577843418550426409405086580581, 248652621703069011230281370429818425958461285 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n) <= A086875(n).
LINKS
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
FORMULA
For prime power q the number of rank-r n X n matrices over GF(q) is F(r, n) = product j=0..(r-1) (q^n-q^j)^2/(q^r-q^j) so a(n) = sum r=1..n r*product j=0..(r-1) (q^n-q^j)^2/(q^r-q^j) . In this case q=2.
a(n) = Sum_{r=1..n} r*Product_{j=0, r-1} (2^n - 2^j)^2/(2^r - 2^j). - Andrew Howroyd, Jul 08 2018
PROG
(PARI) a(n) = {my(q=2); sum(r=1, n, r*prod(j=0, r-1, (q^n-q^j)^2/(q^r-q^j)))} \\ Andrew Howroyd, Jul 08 2018
CROSSREFS
Sequence in context: A012230 A357314 A270505 * A086875 A012211 A297071
KEYWORD
nonn
AUTHOR
Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 24 2003
EXTENSIONS
Terms a(8) and beyond from Andrew Howroyd, Jul 08 2018
STATUS
approved

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Last modified May 28 18:29 EDT 2024. Contains 372919 sequences. (Running on oeis4.)