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 A245561 a(n) = 5^n - ( (sqrt(5)*phi)^n + (sqrt(5)/phi)^n ) + 1, where phi = golden ratio A001622. 1
 0, 1, 11, 76, 451, 2501, 13376, 70001, 361251, 1846876, 9381251, 47437501, 239109376, 1202500001, 6037656251, 30279296876, 151725781251, 759820312501, 3803412109376, 19032656250001, 95219707031251, 476302685546876, 2382252050781251, 11913932617187501 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES Roger L. Bagula, email message, Aug 08 2014. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (11,-40,55,-25). FORMULA a(n) = 5^n - A020876(n) + 1. G.f.: -x*(5*x^2-1)/((1-5*x+5*x^2)*(x-1)*(5*x-1)). -  Vincenzo Librandi, Aug 08 2014 MAPLE g:=n->simplify(rationalize(simplify(expand( (sqrt(5)*p)^n + (sqrt(5)*q)^n ))); # A020876 h:=n->5^n-g(n)+1; [seq(h(n), n=0..40)]; MATHEMATICA CoefficientList[Series[-x (5 x^2 - 1)/((1 - 5 x + 5 x^2) (x - 1)(5 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 08 2014 *) LinearRecurrence[{11, -40, 55, -25}, {0, 1, 11, 76}, 30] (* Harvey P. Dale, Nov 05 2017 *) PROG (MAGMA) [5^n + 1 - Floor(((5+Sqrt(5))/2)^n+((5-Sqrt(5))/2)^n): n in [0..30]]; // Vincenzo Librandi, Aug 08 2014 CROSSREFS Cf. A020876, A001622. Sequence in context: A302382 A034269 A256597 * A056914 A232032 A272395 Adjacent sequences:  A245558 A245559 A245560 * A245562 A245563 A245564 KEYWORD nonn AUTHOR N. J. A. Sloane, Aug 08 2014 STATUS approved

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Last modified August 15 08:32 EDT 2022. Contains 356129 sequences. (Running on oeis4.)