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A268896 Start at a(0)=1. a(n) = a(n-1)+2 if n == 1,2 (mod 3) and a(n)=a(n-1)+a(n-3) if n == 0 (mod 3). 0
1, 3, 5, 6, 8, 10, 16, 18, 20, 36, 38, 40, 76, 78, 80, 156, 158, 160, 316, 318, 320, 636, 638, 640, 1276, 1278, 1280, 2556, 2558, 2560, 5116, 5118, 5120, 10236, 10238, 10240, 20476, 20478, 20480, 40956, 40958 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

See Mathematica section for an explicit formula for the n-th term. - Benedict W. J. Irwin, May 30 2016

LINKS

Table of n, a(n) for n=0..40.

Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-2).

FORMULA

G.f.: ( 1+3*x+5*x^2+3*x^3-x^4-5*x^5 ) / ( (x-1)*(2*x^3-1)*(1+x+x^2) ). - R. J. Mathar, Apr 16 2016

a(3n) = A048487(n). a(3n+1) = A131051(n+1). a(3n+2)=A020714(n). - R. J. Mathar, Apr 16 2016

MATHEMATICA

Simplify[Table[1/6 (10 (2^n)^(1/3) + 4 (-3 + 5 2^(n/3)) Cos[(2 n Pi)/3] + 5 2^((4 + n)/3)Sin[(n Pi)/3] (Sqrt[3] (-1 + 2^(1/3)) Cos[(n Pi)/3] + (1 + 2^(1/3)) Sin[(n Pi)/3]) - 4 (3 + Sqrt[3] Sin[(2 n Pi)/3])), {n, 0, 20}]] (* Benedict W. J. Irwin, May 30 2016 *)

CROSSREFS

Sequence in context: A120243 A304435 A084810 * A014254 A131422 A301744

Adjacent sequences:  A268893 A268894 A268895 * A268897 A268898 A268899

KEYWORD

nonn,easy,less

AUTHOR

Ravesh Sukhram, Feb 27 2016

STATUS

approved

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Last modified September 22 10:53 EDT 2020. Contains 337289 sequences. (Running on oeis4.)