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A154879 Third differences of the Jacobsthal sequence A001045. 8
3, -2, 4, 0, 8, 8, 24, 40, 88, 168, 344, 680, 1368, 2728, 5464, 10920, 21848, 43688, 87384, 174760, 349528, 699048, 1398104, 2796200, 5592408, 11184808, 22369624, 44739240, 89478488, 178956968, 357913944, 715827880, 1431655768, 2863311528, 5726623064 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Second differences of A078008. First differences of the sequence (-1)^(n+1)*A084247(n).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) + a(n+1) = A000079(n), n > 1.

a(n+3) = 8*A001045(n) = 4*A078008(n+1) = 2*A097073(n+1).

From R. J. Mathar, Jan 23 2009: (Start)

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

G.f.: (3-5*x)/((1+x)*(1-2*x)). (End)

a(n) = (1/3)*(8*(-1)^n + 2^n), with n >= 0. - Paolo P. Lava, Mar 02 2009

MATHEMATICA

Differences[LinearRecurrence[{1, 2}, {0, 1}, 40], 3] (* or *) LinearRecurrence[ {1, 2}, {3, -2}, 40] (* Harvey P. Dale, Apr 20 2018 *)

PROG

(MAGMA) [(1/3)*(8*(-1)^n+2^n): n in [0..35]]; // Vincenzo Librandi, Jul 24 2011

CROSSREFS

Cf. A115341.

Sequence in context: A004545 A127481 A284552 * A097673 A226377 A140430

Adjacent sequences:  A154876 A154877 A154878 * A154880 A154881 A154882

KEYWORD

sign,easy

AUTHOR

Paul Curtz, Jan 16 2009

EXTENSIONS

Edited and extended by R. J. Mathar, Jan 23 2009

Typo in A-number in formula corrected by R. J. Mathar, Feb 23 2009

STATUS

approved

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Last modified November 18 11:11 EST 2018. Contains 317302 sequences. (Running on oeis4.)