A245561 a(n) = 5^n - ( (sqrt(5)*phi)^n + (sqrt(5)/phi)^n ) + 1, where phi = golden ratio A001622.

0, 1, 11, 76, 451, 2501, 13376, 70001, 361251, 1846876, 9381251, 47437501, 239109376, 1202500001, 6037656251, 30279296876, 151725781251, 759820312501, 3803412109376, 19032656250001, 95219707031251, 476302685546876, 2382252050781251, 11913932617187501

Offset: 0

Author

N. J. A. Sloane, Aug 08 2014

Keywords

• nonn

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).

Crossrefs

Cf. A020876, A001622.

Programs

Magma

[5^n + 1 - Floor(((5+Sqrt(5))/2)^n+((5-Sqrt(5))/2)^n): n in [0..30]]; // 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 *)

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