A132658 a(6n+k) = 3a(6n+k-1)-3a(6n+k-2)+2a(6n+k-3), k = 0, 1, 3, 4, 5; a(6n+2) = 3a(6n+1)-3a(6n). a(0) = a(1) = 0, a(2) = 1.

0, 0, 1, 3, 6, 11, 21, 42, 63, 105, 210, 441, 903, 1806, 2709, 4515, 9030, 18963, 38829, 77658, 116487, 194145, 388290, 815409, 1669647, 3339294, 5008941, 8348235, 16696470, 35062587, 71794821, 143589642, 215384463, 358974105, 717948210

Offset: 0

Author

Paul Curtz, Nov 15 2007

Keywords

• nonn

Comments

The third differences are 0, 0, 1, 3, 6, -11, 21, 42, 63, 105, 210, -441, ..., equal to the original sequence if each 6th term is negated.

Crossrefs

Cf. A024495.

Programs

Maple

A132658 := proc(n)
    option remember;
    if n <=1 then
        0;
    elif n = 2 then
        1;
    elif modp(n,6) = 2 then
        3*procname(n-1)-3*procname(n-2);
    else
        3*procname(n-1)-3*procname(n-2)+2*procname(n-3) ;
    end if;
end proc:
seq(A132658(n),n=0..80) ; # R. J. Mathar, Aug 07 2017

Mathematica

a[n_] := a[n] = Which[n <= 1, 0, n == 2, 1, Mod[n, 6] == 2, 3a[n-1] - 3a[n-2], True, 3a[n-1] - 3a[n-2] + 2a[n-3]];
Table[a[n], {n, 0, 36}] (* Jean-François Alcover, Oct 27 2023, after R. J. Mathar *)

Extensions

Edited by R. J. Mathar, Jul 07 2008