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).

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

Offset: 0

Author

Ravesh Sukhram, Feb 27 2016

Keywords

• nonn
• easy
• less

Comments

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

Links

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

Programs

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 *)

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