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

1,3

Links

Table of n, a(n) for n=1..72.

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

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

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 *)

Prog

(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

Crossrefs

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

Cf. A131713.

Sequence in context: A058679 A058568 A339769 * A118001 A182414 A256984

Adjacent sequences: A147531 A147532 A147533 * A147535 A147536 A147537

Keyword

easy,nonn

Author

Giovanni Teofilatto, Nov 06 2008

Status

approved