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

0,1

Comments

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

Links

Table of n, a(n) for n=0..31.

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

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

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 *)

Prog

(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 */

Crossrefs

Cf. A130624, A130625.

Sequence in context: A022598 A107635 A132319 * A175796 A115284 A202869

Adjacent sequences: A130623 A130624 A130625 * A130627 A130628 A130629

Keyword

nonn

Author

Paul Curtz, Jun 18 2007

Extensions

Edited and extended by Klaus Brockhaus, Jun 21 2007

Status

approved