A130625 First differences of A130624.

1, 4, 7, 11, 20, 41, 85, 172, 343, 683, 1364, 2729, 5461, 10924, 21847, 43691, 87380, 174761, 349525, 699052, 1398103, 2796203, 5592404, 11184809, 22369621, 44739244, 89478487, 178956971, 357913940, 715827881, 1431655765, 2863311532

Offset: 0

Author

Paul Curtz, Jun 18 2007

Keywords

• nonn

Comments

a(n) = A130624(n+1) - A130624(n).

Links

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

Crossrefs

Cf. A130624, A130626 (second differences).

Programs

Magma

m:=33; 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] ]; [ T[n+1]-T[n]: n in[1..m-1] ]; /* Klaus Brockhaus, Jun 21 2007 */

Mathematica

LinearRecurrence[{3,-3,2},{1,4,7},40] (* Harvey P. Dale, Apr 27 2015 *)

Formula

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

a(n) = 3a(n-1) - 3a(n-2) + 2a(n-3). Sequence is identical to its third differences. Binomial transform of 1, 3, 0. - Paul Curtz, Nov 23 2007

Extensions

Edited and extended by Klaus Brockhaus, Jun 21 2007