A147534 a(n) is congruent to (1,1,2) mod 3.

1, 1, 2, 4, 4, 5, 7, 7, 8, 10, 10, 11, 13, 13, 14, 16, 16, 17, 19, 19, 20, 22, 22, 23, 25, 25, 26, 28, 28, 29, 31, 31, 32, 34, 34, 35, 37, 37, 38, 40, 40, 41, 43, 43, 44, 46, 46, 47, 49, 49, 50, 52, 52, 53, 55, 55, 56, 58, 58, 59, 61, 61, 62, 64, 64, 65, 67, 67, 68, 70, 70, 71

Offset: 1

Author

Giovanni Teofilatto, Nov 06 2008

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A004396 for a(n) congruent to (0, 1, 1) mod 2.

Cf. A131713.

Programs

Magma

I:=[1,1,2]; [n le 3 select I[n] else Self(n-3)+3: n in [1..70]]; // Vincenzo Librandi, Jul 25 2016

Maple

a:=n->add(chrem( [n,j], [1,3] ), j=1..n): seq(a(n)+1, n=-1..70); # Zerinvary Lajos, Apr 08 2009

Mathematica

LinearRecurrence[{1,0,1,-1},{1,1,2,4},80] (* Harvey P. Dale, Dec 09 2012 *)

Formula

a(n) = a(n-3)+3 = n-2/3-A131713(n)/3. G.f.: x*(1+x^2+x^3)/((1-x)^2*(1+x+x^2)). [R. J. Mathar, Nov 07 2008]

a(1)=1, a(2)=1, a(3)=2, a(4)=4, a(n)=a(n-1)+a(n-3)-a(n-4) for n>4. - Harvey P. Dale, Dec 09 2012

a(n) = (3*n - 2 - cos(2*n*Pi/3) + sqrt(3)*sin(2*n*Pi/3))/3. - Wesley Ivan Hurt, Jul 24 2016

a(n) = 1 + floor((n-1)/3) + floor(2*(n-1)/3). - Wesley Ivan Hurt, Jul 25 2016

a(n) = n - sign((n-1) mod 3). - Wesley Ivan Hurt, Sep 25 2017