0,2

The first sequence of "less twisted numbers"; this sequence, A130752 and A130755 form a "suite en trio" (cf. reference, p. 130).

First differences of A130755, second differences of A130752.

Sequence equals its third differences:

1.....3.....8....17....33....64...127...255...512..1025...

...2.....5.....9....16....31....63...128...257...513...

.......3.....4.....7....15....32....65...129...256...

...........1.....3.....8....17....33....64...127...

P. Curtz, Exercise Book, manuscript, 1995.

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

a(0) = 1; a(1) = 3; a(2) = 8; for n > 2, a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3).

a(n) = 2^(n+1) + A128834(n+4).

a(0) = 1; for n > 0, a(n) = 2*a(n-1) + A057079(n-1).

(MAGMA) m:=31; S:=[ [1, 2, 3][(n-1) mod 3 +1]: n in [1..m] ]; [ &+[ Binomial(i-1, k-1)*S[k]: k in [1..i] ]: i in [1..m] ]; /* Klaus Brockhaus, Aug 03 2007 */

(PARI) {m=31; v=vector(m); v[1]=1; v[2]=3; v[3]=8; for(n=4, m, v[n]=3*v[n-1]-3*v[n-2]+2*v[n-3]); v} /* Klaus Brockhaus, Aug 03 2007 */

(PARI) {for(n=0, 30, print1(2^(n+1)+[ -1, -1, 0, 1, 1, 0][n%6+1], ", "))} /* Klaus Brockhaus, Aug 03 2007 */

Cf. A010882 (periodic (1, 2, 3)), A128834 (periodic (0, 1, 1, 0, -1, -1)), A057079 (periodic (1, 2, 1, -1, -2, -1)), A130752 (first differences), A130755 (second differences).

Sequence in context: A001580 A002625 A027181 this_sequence A002626 A029859 A131253

Adjacent sequences: A130747 A130748 A130749 this_sequence A130751 A130752 A130753

nonn

Paul Curtz (bpcrtz(AT)free.fr), Jul 13 2007

Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 03 2007