A132658 - OEIS

%I #10 Oct 27 2023 09:02:44

%S 0,0,1,3,6,11,21,42,63,105,210,441,903,1806,2709,4515,9030,18963,

%T 38829,77658,116487,194145,388290,815409,1669647,3339294,5008941,

%U 8348235,16696470,35062587,71794821,143589642,215384463,358974105,717948210

%N 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.

%C 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.

%p A132658 := proc(n)

%p     option remember;

%p     if n <=1 then

%p         0;

%p     elif n = 2 then

%p         1;

%p     elif modp(n,6) = 2 then

%p         3*procname(n-1)-3*procname(n-2);

%p     else

%p         3*procname(n-1)-3*procname(n-2)+2*procname(n-3) ;

%p     end if;

%p end proc:

%p seq(A132658(n),n=0..80) ; # _R. J. Mathar_, Aug 07 2017

%t 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]];

%t Table[a[n], {n, 0, 80}] (+ _Jean-François Alcover_, Oct 27 2023, after _R. J. Mathar_ *)

%Y Cf. A024495.

%K nonn

%O 0,4

%A _Paul Curtz_, Nov 15 2007

%E Edited by _R. J. Mathar_, Jul 07 2008