A168233 a(n) = 3*n - a(n-1) - 1 for n>0, a(1)=1.

1, 4, 4, 7, 7, 10, 10, 13, 13, 16, 16, 19, 19, 22, 22, 25, 25, 28, 28, 31, 31, 34, 34, 37, 37, 40, 40, 43, 43, 46, 46, 49, 49, 52, 52, 55, 55, 58, 58, 61, 61, 64, 64, 67, 67, 70, 70, 73, 73, 76, 76, 79, 79, 82, 82, 85, 85, 88, 88, 91, 91, 94, 94, 97, 97, 100, 100, 103, 103, 106

Offset: 1

Author

Vincenzo Librandi, Nov 21 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A008585, A001477, A016777, A010674, A016789.

Programs

Magma

[(6*n + 3*(-1)^n + 1)/4: n in [1..70]]; // Vincenzo Librandi, Feb 02 2013

Maple

a:=n->3*floor(n/2)+1; seq(a(k), k = 1..70); # Wesley Ivan Hurt, Feb 01 2013

Mathematica

CoefficientList[Series[(1 + 3*x - x^2)/((1+x) * (1-x)^2), {x, 0, 100}], x] (* Vincenzo Librandi, Feb 02 2013 *)
LinearRecurrence[{1,1,-1},{1,4,4},80] (* Harvey P. Dale, Oct 13 2015 *)

Formula

From Bruno Berselli, Nov 15 2010: (Start)

a(n) = (6*n + 3*(-1)^n + 1)/4.

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

a(n) = a(n-1) + a(n-2) - a(n-3), for n>3.

a(n) + a(n-1) = A016789(n-1) for n>1.

a(n) - a(n-1-2*k) = A010674(n-1) + A008585(k) for n>2*k+1 and k in A001477.

a(n) - a(n-2*k) = A008585(k) for n>2*k and k in A001477. (End)

a(n+1) = A016777(floor((n+1)/2)). - R. J. Mathar, Jan 03 2011

E.g.f.: (1/4)*(3 - 4*exp(x) + (1 + 6*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 16 2016