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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).

a(n)=a(n-1)+2*a(n-2). G.f.: (3-5*x)/((1+x)*(1-2*x)). [R. J. Mathar, Jan 23 2009]

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

MATHEMATICA

A154879[n_Integer] := (2^n - 16 (-1)^n)/6; A154879 /@ Range[50] (* Vladimir Joseph Stephan Orlovsky, Jul 23 2011 *)

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

Corrected typo in A-number in formula R. J. Mathar, Feb 23 2009

STATUS

approved

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Last modified May 23 19:46 EDT 2017. Contains 286926 sequences.