A083336 a(n) = 4*a(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, 1226567328, 3351044259, 4577611587, 12506267433

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

a(n)/A002531(n+1) converges to sqrt(3).

Links

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

Programs

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 *)

Formula

a(2*n) = A082841(n) = a(2*n-1) + 3*A002531(2*n).

a(2*n+1) = (a(2*n) + 3*A002531(2*n+1)) / 2.

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