A137719 Sequence based on the pattern [3n, 3n, 3n, 3n+2, 3n+1, 3n+2].

0, 2, 1, 2, 3, 3, 3, 5, 4, 5, 6, 6, 6, 8, 7, 8, 9, 9, 9, 11, 10, 11, 12, 12, 12, 14, 13, 14, 15, 15, 15, 17, 16, 17, 18, 18, 18, 20, 19, 20, 21, 21, 21, 23, 22, 23, 24, 24, 24, 26, 25, 26, 27, 27, 27, 29, 28, 29, 30, 30, 30, 32, 31, 32, 33, 33, 33, 35, 34

Offset: 0

Author

Paul Barry, Feb 08 2008

Keywords

• easy
• nonn

Comments

Powers of 2 in a scaled version of the Hankel transform of A106191.

Links

• M. F. Hasler, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,-1).

Crossrefs

Cf. A106191, A137718.

Programs

Magma

[&+[(2*n-i) mod 3: i in [0..Floor(n/2)]]: n in [0..80]]; // Wesley Ivan Hurt, Mar 21 2016

Maple

A137719:=n->add(2*n-i mod 3, i=0..floor(n/2)): seq(A137719(n), n=0..100); # Wesley Ivan Hurt, Mar 21 2016

Mathematica

Table[Sum[Mod[2 n - i, 3], {i, 0, Floor[n/2]}], {n, 0, 80}] (* Wesley Ivan Hurt, Mar 21 2016 *)

PARI

apply( A137719(n)={(n=divrem(n-1,6))[1]*3+min(n[2]+2*!n[2],3)}, [0..30]) \\ M. F. Hasler, Oct 27 2019

Formula

a(n) = log(abs(A137718(n)))/log(2).

From R. J. Mathar, Feb 10 2008: (Start)

O.g.f.: 1/(2*(x-1)^2) + (x-1)/(3*(x^2+x+1)) - 1/(4*(x+1)) - 1/(12*(x-1)).

a(n) = 3 + a(n-6). (End)

From Colin Barker, Jun 27 2013: (Start)

a(n) = a(n-2) + a(n-3) - a(n-5).

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

a(n) = Sum_{i=0..floor(n/2)} (2n-i mod 3). - Wesley Ivan Hurt, Mar 22 2016

a(n) = A004526(n+1) + A079978(n). - R. J. Mathar, Oct 27 2019