A163227 Fibonacci-accumulation sequence.

1, 1, 1, 2, 2, 4, 3, 7, 5, 12, 8, 20, 13, 33, 21, 54, 34, 88, 55, 143, 89, 232, 144, 376, 233, 609, 377, 986, 610, 1596, 987, 2583, 1597, 4180, 2584, 6764, 4181, 10945, 6765, 17710, 10946, 28656, 17711, 46367, 28657, 75024, 46368, 121392, 75025, 196417

Offset

1,4

Comments

Accumulation of A000045 and A000071.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,2,0,0,0,-1).

Formula

a(n) = 2*a(n-2) - a(n-6), where a(1,2,3)=1.

G.f.: x*(1 + x - x^2)/(1 - 2*x^2 + x^6). - G. C. Greubel, Dec 11 2016

Mathematica

LinearRecurrence[{0, 2, 0, 0, 0, -1}, {1, 1, 1, 2, 2, 4}, 50] (* or *) CoefficientList[Series[x*(1 + x - x^2)/(1 - 2*x^2 + x^6), {x, 1, 50}], x] (* G. C. Greubel, Dec 11 2016 *)

Prog

(PARI) Vec(x*(1 + x - x^2)/(1 - 2*x^2 + x^6) + O(x^50)) \\ G. C. Greubel, Dec 11 2016
(Magma) m:=55; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+x-x^2)/(1-2*x^2+x^6))); // Vincenzo Librandi, Dec 12 2016

Crossrefs

Cf. A000071, A000045, A097110.

Sequence in context: A238622 A096441 A100824 * A325690 A238779 A239832

Adjacent sequences: A163224 A163225 A163226 * A163228 A163229 A163230

Keyword

nonn,easy

Author

Mark Dols, Jul 23 2009

Status

approved