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

Author

Mark Dols, Jul 23 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000071, A000045, A097110.

Programs

Magma

m:=55; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+x-x^2)/(1-2*x^2+x^6))); // Vincenzo Librandi, Dec 12 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 *)

PARI

Vec(x*(1 + x - x^2)/(1 - 2*x^2 + x^6) + O(x^50)) \\ G. C. Greubel, Dec 11 2016

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