A196468 a(1)=11; a(n) = floor((2 + sqrt(8))*a(n-1)) for n > 1.

11, 53, 255, 1231, 5943, 28695, 138551, 668983, 3230135, 15596471, 75306423, 363611575, 1755671991, 8477134263, 40931225015, 197633437111, 954258648503, 4607568342455, 22247307963831, 107419505225143, 518667252755895, 2504347031924151, 12092057138720183

Offset: 1

Author

Philippe Deléham, Oct 02 2011

Keywords

• nonn
• easy

Comments

Contains only odd numbers.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..150
• Index entries for linear recurrences with constant coefficients, signature (5,0,-4).

Crossrefs

Cf. A057087, A086843, A086844.

Programs

Magma

I:=[11,53,255]; [n le 3 select I[n] else 5*Self(n-1)-4*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Oct 05 2011

Mathematica

NestList[Floor[(2+Sqrt[8])#]&,11,30] (* or *) LinearRecurrence[{5,0,-4},{11,53,255},30] (* Harvey P. Dale, Nov 18 2013 *)

Formula

G.f.: -x*(-11 + 2*x + 10*x^2) / ( (x-1)*(4*x^2 + 4*x - 1) ).

a(n) = (2 + 33*A057087(n) + 20*A057087(n-1))/14. - R. J. Mathar, Oct 04 2011