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A296605 Rectangle read by rows: T(n,k) is the number of n X n diagonalizable matrices over GF(3) that have exactly k distinct eigenvalues, n >= 0, 0 <= k <= 3. 1
1, 0, 0, 0, 0, 3, 0, 0, 0, 3, 36, 0, 0, 3, 702, 1404, 0, 3, 38070, 379080, 0, 3, 5351346, 341368830, 0, 3, 2434569858, 1231457092866, 0, 3, 2987199920970, 17481694843567584, 0, 3, 11966842794993066, 1077553466091961763220 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..35.

Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

FORMULA

T(n,k)/A053290(n) is the coefficient of y^(3-k)*x^n in the expansion of (-1 + y + Sum_{n>=0} x^n/A053290(n))^3.

EXAMPLE

Array begins:

  1, 0,       0,         0,

  0, 3,       0,         0,

  0, 3,      36,         0,

  0, 3,     702,      1404,

  0, 3,   38070,    379080,

  0, 3, 5351346, 341368830

MATHEMATICA

nn = 8; g[ n_] := (q - 1)^n  q^Binomial[n, 2] FunctionExpand[

    QFactorial[n, q]] /. q -> 3; G[u_, z_] := Sum[z^k/\[Gamma][k], {k, 0, nn}] - 1 + u ; Grid[Map[Reverse, Table[\[Gamma][n], {n, 0, nn}] CoefficientList[Series[G[u, z]^3, {z, 0, nn}], {z, u}]]]

CROSSREFS

Cf. A290516 (row sums).

Sequence in context: A007514 A151671 A267502 * A278478 A122480 A096133

Adjacent sequences:  A296602 A296603 A296604 * A296606 A296607 A296608

KEYWORD

nonn,tabf

AUTHOR

Geoffrey Critzer, Dec 16 2017

STATUS

approved

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Last modified February 19 16:23 EST 2018. Contains 299356 sequences. (Running on oeis4.)