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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 November 12 04:21 EST 2019. Contains 329051 sequences. (Running on oeis4.)