

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
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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.: (36*x+4*x^2)/((12*x)*(1x+x^2)).
a(n) = 3a(n1)  3a(n2) + 2a(n3).  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][ (n1) mod 3 +1 ]: n in [1..m] ]; T:=[ &+[ Binomial(i1, k1)*S[k]: k in [1..i] ]: i in [1..m] ]; U:=[ T[n+1]T[n]: n in[1..m1] ]; [ U[n+1]U[n]: n in[1..m2] ]; /* 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



