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 A189318 Expansion of 5*(1-2*x)/(1-3*x-2*x^2+4*x^3) 5
 5, 5, 25, 65, 225, 705, 2305, 7425, 24065, 77825, 251905, 815105, 2637825, 8536065, 27623425, 89391105, 289275905, 936116225, 3029336065, 9803137025, 31723618305, 102659784705, 332214042625, 1075067224065, 3478990618625, 11258250133505 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS (Start) Let A be the unit-primitive matrix (see [Jeffery]) A=A_(10,4)= (0 0 0 0 1) (0 0 0 2 0) (0 0 2 0 1) (0 2 0 2 0) (2 0 2 0 1). Then a(n)=Trace(A^n). (End) Evidently one of a class of accelerator sequences for Catalan's constant based on traces of successive powers of a unit-primitive matrix A_(N,r) (03, a(0)=5, a(1)=5, a(2)=25, a(3)=65. a(n)=Sum_{k=1..5} ((w_k)^4-3*(w_k)^2+1)^n, w_k=2*cos((2*k-1)*Pi/10). a(n)=1+2*(1-Sqrt(5))^n+2*(1+Sqrt(5))^n. a(n)=5*A052899(n). MATHEMATICA CoefficientList[Series[5(1-2x)/(1-3x-2x^2+4x^3), {x, 0, 30}], x] (* or *) LinearRecurrence[{3, 2, -4}, {5, 5, 25}, 30] (* Harvey P. Dale, Jun 02 2014 *) PROG (PARI) Vec(5*(1-2*x)/(1-3*x-2*x^2+4*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 25 2012 CROSSREFS Cf. A052899. Sequence in context: A257607 A093643 A223263 * A257615 A257624 A176160 Adjacent sequences:  A189315 A189316 A189317 * A189319 A189320 A189321 KEYWORD nonn,easy AUTHOR L. Edson Jeffery, Apr 20 2011 STATUS approved

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Last modified June 26 04:11 EDT 2019. Contains 324369 sequences. (Running on oeis4.)