A129929 - OEIS

A129929

Binomial transform of the periodic sequence with periodic pattern 1,1,1,0,0.

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

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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: A023427 A216116 A357926 * A360891 A073738 A137631

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