A154570 The main diagonal of the successive differences of A154127.

1, 3, -4, 2, -6, -2, -14, -18, -46, -82, -174, -338, -686, -1362, -2734, -5458, -10926, -21842, -43694, -87378, -174766, -349522, -699054, -1398098, -2796206, -5592402, -11184814, -22369618, -44739246, -89478482, -178956974, -357913938, -715827886

Offset

0,2

Links

Table of n, a(n) for n=0..32.

Index entries for linear recurrences with constant coefficients, signature (1, 2).

Formula

a(n) = a(n-1) + 2*a(n-2), n>0.

a(n+2) = 2*(-1)^(n+1)*A140966(n).

a(n+5) = -2*A083582(n).

a(2n+1) = 3 - A078008(2n) = 3 - A047849(n).

a(2n+2) = -4 - A078008(2n+1) = -4 - A020988(n).

G.f.: (1+2*x-9*x^2)/((1+x)*(1-2*x)). - R. J. Mathar, Feb 25 2009

Mathematica

f[n_]:=2/(n+1); x=6; Table[x=f[x]; Numerator[x], {n, 0, 5!}](* Absolute Values *) (* Vladimir Joseph Stephan Orlovsky, Mar 12 2010 *)

Prog

(PARI) a(n)=if(n, ([0, 1; 2, 1]^(n-1)*[3; -4])[1, 1], 1) \\ Charles R Greathouse IV, May 26 2026

Crossrefs

Cf. A020988, A047849, A078008, A083582, A140966, A154127.

Sequence in context: A179297 A133620 A322965 * A145961 A369557 A375486

Adjacent sequences: A154567 A154568 A154569 * A154571 A154572 A154573

Keyword

sign,easy,changed

Author

Paul Curtz, Jan 12 2009

Extensions

Edited and extended by R. J. Mathar, Feb 25 2009

Status

approved