A373784 Number of n X n periodic matrices over GF(3).
1, 3, 73, 17083, 36899281, 723299706163, 127954611219059353, 203907700711025670584683, 2925406687944886208690683289761, 377768302929213133608351637048047649123, 439058106335101098121200963942043393433721555433, 4592676942963368381676178826582121303149079572759596838683
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Periodic Matrix
Programs
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Mathematica
nn = 11; B[n_] := Product[q^n - q^i, {i, 0, n - 1}]/(q - 1)^n /. q -> 3; e[x_] := Sum[x^n/B[n], {n, 0, nn}];f[x_] := Sum[(q - 1)^n x^n, {n, 0, nn}] /. q -> 3; Table[B[n], {n, 0, nn}] CoefficientList[Series[e[x] f[ x], {x, 0, nn}], x]
Formula
Sum_{n>=0}a_n*x^n/B(n) = e(x)*f(x) where B(n) = A053290(n)/2^n, e(x) = Sum{n>=0}x^n/B(n) and f(x) = Sum_{n>=0} (2x)^n.
Comments