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%I #16 Aug 18 2015 00:39:16
%S 1,2,4,7,11,17,29,58,129,292,639,1333,2666,5188,9999,19388,38166,
%T 76332,154261,312703,632171,1271107,2542214,5066717,10087066,20099107,
%U 40123189,80246378,160689174,321892577,644617194,1290066428,2580132856
%N Binomial transform of the periodic sequence with periodic pattern 1,1,1,0,0.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,2).
%F a(n)=5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+2a(n-5). - _R. J. Mathar_, Mar 06 2008
%F 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
%e The sequence and first, 2nd, etc. difference are
%e 1..2..4..7..11..17..29...58..129..292..639.1333..2666
%e ..1..2..3..4...6..12..29...71......
%e ....1..1..1..2...6...17.42......
%e ......0..0..1..4...11..25.....
%e ........0..1..3...7..14.....
%e ..........1..2..4...7.........<= original series 5 rows above reappears
%e .......... the leading edge of the difference triangle is 5-periodic 1,1,1,0,0.
%p 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
%t LinearRecurrence[{5,-10,10,-5,2},{1,2,4,7,11},40] (* _Harvey P. Dale_, Oct 08 2012 *)
%K nonn,easy,less
%O 0,2
%A _Paul Curtz_, Jun 06 2007, Jun 20 2007
%E Edited by _R. J. Mathar_, Mar 06 2008
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