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A129929 Binomial transform of the periodic sequence with periodic pattern 1,1,1,0,0. 2
1, 2, 4, 7, 11, 17, 29, 58, 129, 292, 639, 1333, 2666, 5188, 9999, 19388, 38166, 76332, 154261, 312703, 632171, 1271107, 2542214, 5066717, 10087066, 20099107, 40123189, 80246378, 160689174, 321892577, 644617194, 1290066428, 2580132856 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,2).

FORMULA

a(n)=5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+2a(n-5). - R. J. Mathar, Mar 06 2008

G.f.:-(x^2-x+1)*(x-1)^2/((2*x-1)*(x^4-2*x^3+4*x^2-3*x+1)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009

EXAMPLE

The sequence and first, 2nd, etc. difference are

1..2..4..7..11..17..29...58..129..292..639.1333..2666

..1..2..3..4...6..12..29...71......

....1..1..1..2...6...17.42......

......0..0..1..4...11..25.....

........0..1..3...7..14.....

..........1..2..4...7.........<= original series 5 rows above reappears

.......... the leading edge of the difference triangle is 5-periodic 1,1,1,0,0.

MAPLE

A129929 := proc(n) option remember ; if n <= 4 then op(n+1, [1, 2, 4, 7, 11]) ; else 5*A129929(n-1)-10*A129929(n-2)+10*A129929(n-3)-5*A129929(n-4)+2*A129929(n-5) ; fi ; end: seq(A129929(n), n=0..80) ; # R. J. Mathar, Mar 06 2008

MATHEMATICA

LinearRecurrence[{5, -10, 10, -5, 2}, {1, 2, 4, 7, 11}, 40] (* Harvey P. Dale, Oct 08 2012 *)

CROSSREFS

Sequence in context: A152398 A023427 A216116 * A073738 A137631 A003403

Adjacent sequences:  A129926 A129927 A129928 * A129930 A129931 A129932

KEYWORD

nonn,easy,less

AUTHOR

Paul Curtz, Jun 06 2007, Jun 20 2007

EXTENSIONS

Edited by R. J. Mathar, Mar 06 2008

STATUS

approved

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Last modified June 18 18:09 EDT 2021. Contains 345120 sequences. (Running on oeis4.)