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
Offset: 0
Examples
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.
Links
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,2).
Programs
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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
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Mathematica
LinearRecurrence[{5,-10,10,-5,2},{1,2,4,7,11},40] (* Harvey P. Dale, Oct 08 2012 *)
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
Extensions
Edited by R. J. Mathar, Mar 06 2008