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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 Geoffrey Critzer, Combinatorics of Vector Spaces over Finite Fields, Master's thesis, Emporia State University, 2018. 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 October 15 00:14 EDT 2019. Contains 328025 sequences. (Running on oeis4.)