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A163227 Fibonacci-accumulation sequence. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 28 11:40 EDT 2020. Contains 334681 sequences. (Running on oeis4.)