A130626 Second differences of A130624.

3, 3, 4, 9, 21, 44, 87, 171, 340, 681, 1365, 2732, 5463, 10923, 21844, 43689, 87381, 174764, 349527, 699051, 1398100, 2796201, 5592405, 11184812, 22369623, 44739243, 89478484, 178956969, 357913941, 715827884, 1431655767, 2863311531

Offset: 0

Author

Paul Curtz, Jun 18 2007

Keywords

• nonn

Comments

First differences of A130625: a(n) = A130625(n+1) - A130625(n).

Links

• Index entries for linear recurrences with constant coefficients, signature (3, -3, 2).

Crossrefs

Cf. A130624, A130625.

Programs

Magma

m:=34; S:=[ [0, 1, 3][ (n-1) mod 3 +1 ]: n in [1..m] ]; T:=[ &+[ Binomial(i-1, k-1)*S[k]: k in [1..i] ]: i in [1..m] ]; U:=[ T[n+1]-T[n]: n in[1..m-1] ]; [ U[n+1]-U[n]: n in[1..m-2] ]; /* Klaus Brockhaus, Jun 21 2007 */

Mathematica

Differences[LinearRecurrence[{3,-3,2},{0,1,5},40],2] (* or *) LinearRecurrence[{3,-3,2},{3,3,4},40] (* Harvey P. Dale, Aug 05 2024 *)

Formula

G.f.: (3-6*x+4*x^2)/((1-2*x)*(1-x+x^2)).

a(n) = 3a(n-1) - 3a(n-2) + 2a(n-3). - Paul Curtz, Apr 24 2008

Extensions

Edited and extended by Klaus Brockhaus, Jun 21 2007