A166138 Trisection A022998(3n+1).

1, 8, 7, 20, 13, 32, 19, 44, 25, 56, 31, 68, 37, 80, 43, 92, 49, 104, 55, 116, 61, 128, 67, 140, 73, 152, 79, 164, 85, 176, 91, 188, 97, 200, 103, 212, 109, 224, 115, 236, 121, 248, 127, 260, 133, 272, 139, 284, 145, 296, 151, 308, 157, 320, 163, 332, 169, 344, 175, 356, 181, 368, 187, 380, 193, 392

Offset: 0

Author

Paul Curtz, Oct 08 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Crossrefs

Cf. A165988, A166304.

Programs

Mathematica

LinearRecurrence[{0,2,0,-1},{1,8,7,20},70] (* Harvey P. Dale, Aug 15 2012 *)
Table[If[OddQ@ #, #, 2 #] &[3 n + 1], {n, 0, 65}] (* or *)
CoefficientList[Series[(1 + 8 x + 5 x^2 + 4 x^3)/((1 - x)^2 (1 + x)^2), {x, 0, 65}], x] (* Michael De Vlieger, Apr 27 2016 *)

Formula

a(2n) = 6n+1 = A016921(n).

a(2n+1) = 12n+8 = A017617(n).

a(n) = 2*a(n-2)-a(n-4) = (3n+1)*(3-(-1)^n)/2.

From G. C. Greubel, Apr 26 2016: (Start)

O.g.f.: (1 + 8*x + 5*x^2 + 4*x^3)/((1 - x)^2*(1 + x)^2).

E.g.f.: (1/2)*(-1 + 3*x + (3+9*x)*exp(2*x))*exp(-x). (End)