A083336 a(n)=4a(n-2)-a(n-4).

3, 3, 9, 12, 33, 45, 123, 168, 459, 627, 1713, 2340, 6393, 8733, 23859, 32592, 89043, 121635, 332313, 453948, 1240209, 1694157, 4628523, 6322680, 17273883, 23596563, 64467009, 88063572, 240594153, 328657725, 897909603

Offset

0,1

Comments

a(n)/A002531(n+1) converges to sqrt(3). a(2n)=A082841(n). a(2n)=a(2n-1)+ 3*A002531(2n). a(2n+1)=(1/2)(a(2n)+3*A002531(2n+1)).

Links

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (0, 4, 0, -1).

Formula

G.f.: (3+3x-3x^2)/(1-4x^2+x^4)

Mathematica

CoefficientList[Series[(3+3x-3x^2)/(1-4x^2+x^4), {x, 0, 30}], x]
Transpose[NestList[Flatten[{Rest[#], 4#[[3]]-First[#]}]&, {3, 3, 9, 12}, 50]][[1]]  (* Harvey P. Dale, Mar 26 2011 *)
LinearRecurrence[{0, 4, 0, -1}, {3, 3, 9, 12}, 30] (* T. D. Noe, Mar 26 2011 *)

Crossrefs

Sequence in context: A325243 A319271 A066314 * A225436 A183811 A303640

Adjacent sequences: A083333 A083334 A083335 * A083337 A083338 A083339

Keyword

easy,nonn

Author

Mario Catalani (mario.catalani(AT)unito.it), Apr 26 2003

Status

approved