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A289538 Expected dimension of the null space of a random linear operator on an n-dimensional vector space over the field with two elements as n -> infinity. 4
8, 5, 0, 1, 7, 9, 8, 3, 0, 8, 7, 3, 9, 7, 9, 3, 3, 2, 8, 7, 6, 0, 6, 3, 2, 8, 1, 4, 9, 3, 5, 9, 1, 8, 7, 8, 8, 4, 0, 4, 2, 6, 7, 2, 5, 9, 7, 3, 2, 0, 2, 7, 2, 5, 9, 8, 7, 3, 5, 8, 0, 5, 2, 5, 5, 6, 3, 0, 9, 5, 9, 4, 1, 1, 8, 3, 3, 1, 3, 4, 4, 3, 6, 3, 0, 4, 1, 0, 6, 7, 0, 8, 8, 5, 9, 3, 5, 6, 5, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
More precisely, let X:L(V) -> {0,1,2,...,n} be the random variable that assigns to each linear operator T on n-dimensional vector space V over F_2, the integer j in {0,1,2,...,n} such that the dimension of the null space of T = j. Then E(X) = 0.850179183...
LINKS
FORMULA
Let A(x) = Sum_{n>=0} Product_{i>=n+1} (1-1/2^i)*x^n/A002884(n). Then A'(1) = 0.85017983...
MATHEMATICA
nn = 300; q := 2; A[x_] := Sum[1/(FunctionExpand[QFactorial[j, q]] (q - 1)^j q^Binomial[j, 2]) Product[1 - 1/q^i, {i, j + 1, \[Infinity]}] x^j, {j, 0, nn}]; RealDigits[
N[Normal[Series[D[A[x], x] /. x -> 1, {x, 0, nn}]], 100]][[1]]
CROSSREFS
Sequence in context: A096687 A326955 A199374 * A154224 A257575 A154165
KEYWORD
cons,nonn
AUTHOR
Geoffrey Critzer, Jul 10 2017
STATUS
approved

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Last modified August 12 19:26 EDT 2024. Contains 375113 sequences. (Running on oeis4.)