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A130626 Second differences of A130624. 2
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 (list; graph; refs; listen; history; text; internal format)
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.

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

a(n) = (5/6)*(1/2-(1/2)*i*sqrt(3))^n + (5/6)*(1/2+(1/2)*i*sqrt(3))^n + (4/3)*2^n - (1/6)*i*(1/2-(1/2)*i*sqrt(3))^n*sqrt(3) + (1/6)*i*(1/2+(1/2)*i*sqrt(3))^n*sqrt(3), with n >= 0 and i=sqrt(-1). - Paolo P. Lava, Jun 12 2008

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

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Last modified May 31 16:29 EDT 2020. Contains 334748 sequences. (Running on oeis4.)