OFFSET
0,2
COMMENTS
T is a periodic matrix if T = T^k for some k > 1. T is periodic iff image(T) = image(T^2) iff x^2 does not divide the minimal polynomial of T.
LINKS
Eric Weisstein's World of Mathematics, Periodic Matrix
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.
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]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Jun 18 2024
STATUS
approved