A196472 a(1)=1; a(n) = floor((3 + sqrt(21))*a(n-1)/2) for n > 1.

1, 3, 11, 41, 155, 587, 2225, 8435, 31979, 121241, 459659, 1742699, 6607073, 25049315, 94969163, 360055433, 1365073787, 5175387659, 19621384337, 74390315987, 282035100971, 1069276250873, 4053934055531, 15369630919211, 58270694924225, 220920977530307, 837575017363595

Offset: 1

Author

Philippe Deléham, Oct 03 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 (4,0,-3).

Crossrefs

Cf. A108306.

Programs

Magma

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

Mathematica

With[{c=(3+Sqrt[21])/2},NestList[Floor[c*#]&,1,30]] (* Harvey P. Dale, Apr 23 2014 *)

Formula

G.f.: -x*(-1+ x + x ^2) / ( (x-1)*(3*x^2 + 3*x - 1) ). - R. J. Mathar, Oct 04 2011

a(n) = (3 + 2*A108306(n))/15. - R. J. Mathar, Oct 04 2011