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A249693 a(4n) = 3*n+1, a(2n+1) = 3*n+2, a(4n+2) = 3*n. 1
1, 2, 0, 5, 4, 8, 3, 11, 7, 14, 6, 17, 10, 20, 9, 23, 13, 26, 12, 29, 16, 32, 15, 35, 19, 38, 18, 41, 22, 44, 21, 47, 25, 50, 24, 53, 28, 56, 27, 59, 31, 62, 30, 65, 34, 68, 33, 71, 37, 74, 36, 77, 40, 80, 39, 83, 43, 86, 42, 89, 46, 92, 45 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A permutation of the nonnegative numbers.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

FORMULA

a(n+4) = a(n) + (sequence of period 2: repeat 3, 6).

a(4n+1) = 2*a(4n).

a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12).

a(n) is the rank of A061037(n) = -1, -3, 0, 5, ... in A247829(n) = 0, -1, -3, 2, ... .

G.f.: (1 + 2*x - x^2 + 3*x^3 + 3*x^4 + x^5)/(1 - x^2 - x^4 + x^6).

a(n) = (1 + 9*n - 3*(n+1)*(-1)^n + 10*cos(n*Pi/2))/8. - Robert Israel, Dec 03 2014

MATHEMATICA

a[n_] := (1/8)*(3*(-1)^(n+1)*(n+1)+9*n+10*{1, 0, -1, 0}[[Mod[n, 4]+1]]+1); Table[a[n], {n, 0, 100}] (* Jean-Fran├žois Alcover, Dec 04 2014, after Robert Israel *)

PROG

(PARI) x='x+O('x^75); Vec((1 + 2*x - x^2 + 3*x^3 + 3*x^4 + x^5)/(1 - x^2 - x^4 + x^6)) \\ G. C. Greubel, Sep 20 2018

(MAGMA) m:=75; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 + 2*x - x^2 + 3*x^3 + 3*x^4 + x^5)/(1 - x^2 - x^4 + x^6))); // G. C. Greubel, Sep 20 2018

CROSSREFS

Cf. A001477, A010704, A010857, A016789, A061037.

Sequence in context: A215481 A262933 A197253 * A251420 A137421 A155524

Adjacent sequences:  A249690 A249691 A249692 * A249694 A249695 A249696

KEYWORD

nonn

AUTHOR

Paul Curtz, Dec 03 2014

STATUS

approved

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Last modified October 20 20:24 EDT 2019. Contains 328273 sequences. (Running on oeis4.)