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 A189334 Expansion of (1-6*x+x^2)/(1-10*x+5*x^2) 1
 1, 4, 36, 340, 3220, 30500, 288900, 2736500, 25920500, 245522500, 2325622500, 22028612500, 208658012500, 1976437062500, 18721080562500, 177328620312500, 1679680800312500, 15910164901562500, 150703245014062500, 1427481625632812500 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS (Start) Let A be the unit-primitive matrix (see [Jeffery]) A=A_(10,3)= (0 0 0 1 0) (0 0 1 0 1) (0 1 0 2 0) (1 0 2 0 1) (0 2 0 2 0). Then a(n)=(1/5)*Trace(A^(2*n)). (See also A189317.) (End) Evidently one of a class of accelerator sequences for Catalan's constant based on traces of successive powers (here they are A^(2*n)) of a unit-primitive matrix A_(N,r) (02, a(0)=1, a(1)=4, a(2)=36. a(n)=(1/5)*Sum_{k=1..5) ((w_k)^3-2*w_k)^(2*n), w_k=2*cos((2*k-1)*Pi/10). CROSSREFS A189315, A189316, A189317, A189318. Sequence in context: A226283 A270473 A288269 * A026334 A247562 A168595 Adjacent sequences: A189331 A189332 A189333 * A189335 A189336 A189337 KEYWORD nonn AUTHOR L. Edson Jeffery, Apr 20 2011 STATUS approved

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Last modified February 5 11:26 EST 2023. Contains 360084 sequences. (Running on oeis4.)