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A130626 Second differences of A130624. 2

%I

%S 3,3,4,9,21,44,87,171,340,681,1365,2732,5463,10923,21844,43689,87381,

%T 174764,349527,699051,1398100,2796201,5592405,11184812,22369623,

%U 44739243,89478484,178956969,357913941,715827884,1431655767,2863311531

%N Second differences of A130624.

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

%F G.f.: (3-6*x+4*x^2)/((1-2*x)*(1-x+x^2)).

%F a(n) = 3a(n-1) - 3a(n-2) + 2a(n-3). - _Paul Curtz_, Apr 24 2008

%F 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

%o (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 */

%Y Cf. A130624, A130625.

%K nonn

%O 0,1

%A _Paul Curtz_, Jun 18 2007

%E Edited and extended by _Klaus Brockhaus_, Jun 21 2007

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Last modified July 4 16:24 EDT 2020. Contains 335448 sequences. (Running on oeis4.)