A135575 a(n) = A135574(n+1) - 2*A135574(n).
0, 3, -5, 9, -16, 30, -63, 129, -257, 513, -1024, 2046, -4095, 8193, -16385, 32769, -65536, 131070, -262143, 524289, -1048577, 2097153, -4194304, 8388606, -16777215, 33554433, -67108865, 134217729, -268435456, 536870910, -1073741823, 2147483649, -4294967297, 8589934593
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (-2,-1,-2,-1,-2).
Programs
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Maple
A024495 := proc(n) option remember ; if n <=1 then 0 ; elif n = 2 then 1; elif n = 3 then 3 ; else A024495(n-1)-A024495(n-2)+2^(n-2) ; fi ; end: A135574 := proc(n) option remember ; A024495(2*floor(n/2)+1 - ( n mod 2)) ; end: A135575 := proc(n) A135574(n+1)-2*A135574(n) ; end: seq(A135575(n),n=0..80) ; # R. J. Mathar, Mar 31 2008
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Mathematica
LinearRecurrence[{-2, -1, -2, -1, -2}, {0, 3, -5, 9, -16}, 25] (* G. C. Greubel, Oct 19 2016 *) -
PARI
a(n)=([0,1,0,0,0; 0,0,1,0,0; 0,0,0,1,0; 0,0,0,0,1; -2,-1,-2,-1,-2]^n*[0;3;-5;9;-16])[1,1] \\ Charles R Greathouse IV, Oct 19 2016
Formula
G.f.: x*(3*x^3+2*x^2+x+3)/((2*x+1)*(x^2+x+1)*(x^2-x+1)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009
a(n) + 2*a(n-1) + a(n-2) + 2*a(n-3) + a(n-4) + 2*a(n-5) = 0. - G. C. Greubel, Oct 19 2016
Extensions
More terms from R. J. Mathar, Mar 31 2008