A186272 The sum of the Fibonacci and shifted tribonacci sequences.

1, 1, 2, 3, 4, 8, 13, 22, 38, 65, 112, 194, 337, 588, 1030, 1811, 3196, 5660, 10057, 17926, 32046, 57445, 103236, 185962, 335697, 607184, 1100186, 1996699, 3629044, 6604536, 12033861, 21949630, 40073798, 73225249, 133902408, 245023146, 448626225, 821848892, 1506270798

Offset

1,3

Comments

Limit ratio is 1.839286755214161 ...

Last digit sequence has a period of 1860, starting from 3rd element.

Links

Table of n, a(n) for n=1..39.

Index entries for linear recurrences with constant coefficients, signature (2,1,-1,-2,-1).

Formula

a(n) = A000045(n-1) + A000213(n-3).

G.f.: x+x^2 -x^3*(1+x)*(x^2+3*x-2) / ( (x^2+x-1)*(x^3+x^2+x-1) ). - R. J. Mathar, Feb 16 2011

Example

a(10) = 65 = Fib(9) + Trib(7) = 34 + 31.

Mathematica

Rest[CoefficientList[Series[x+x^2-x^3(1+x)(x^2+3*x-2)/((x^2+x-1)(x^3+x^2+x-1)), {x, 0, 50}], x]]  (* Harvey P. Dale, Feb 24 2011 *)

Crossrefs

Cf. A000045, A000213.

Sequence in context: A219968 A126042 A076227 * A361722 A092075 A091415

Adjacent sequences: A186269 A186270 A186271 * A186273 A186274 A186275

Keyword

nonn,changed

Author

Carmine Suriano, Feb 16 2011

Status

approved