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

0,2

Comments

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

Mathematica

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

Prog

(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 */

Crossrefs

Cf. A130624, A130626 (second differences).

Sequence in context: A083839 A091176 A002974 * A104102 A074705 A352216

Adjacent sequences: A130622 A130623 A130624 * A130626 A130627 A130628

Keyword

nonn

Author

Paul Curtz, Jun 18 2007

Extensions

Edited and extended by Klaus Brockhaus, Jun 21 2007

Status

approved