A309214 a(0)=0; thereafter a(n) = a(n-1)+n if a(n-1) even, otherwise a(n) = a(n-1)-n.
0, 1, -1, -4, 0, 5, -1, -8, 0, 9, -1, -12, 0, 13, -1, -16, 0, 17, -1, -20, 0, 21, -1, -24, 0, 25, -1, -28, 0, 29, -1, -32, 0, 33, -1, -36, 0, 37, -1, -40, 0, 41, -1, -44, 0, 45, -1, -48, 0, 49, -1, -52, 0, 53, -1, -56, 0, 57, -1, -60, 0, 61, -1, -64, 0, 65, -1, -68, 0, 69, -1, -72, 0, 73, -1
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (1,-2,2,-1,1).
Programs
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Maple
t:=0; a:=[t]; M:=100; for i from 1 to M do if (t mod 2) = 0 then t:=t+i else t:=t-i; fi; a:=[op(a),t]; od: a;
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PARI
concat(0, Vec(x*(1 - 2*x - x^2) / ((1 - x)*(1 + x^2)^2) + O(x^80))) \\ Colin Barker, Aug 13 2019
Formula
a(4t)=0, a(4t+1)=4t+1, a(4t+2)=-1, a(4t+3)=-(4t+4).
From Colin Barker, Aug 13 2019: (Start)
G.f.: x*(1 - 2*x - x^2) / ((1 - x)*(1 + x^2)^2).
a(n) = a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) + a(n-5) for n>4.
a(n) = (-2 + (1+i)*(-i)^n + (1-i)*i^n + 2*i*((-i)^n-i^n)*n) / 4 where i=sqrt(-1).
(End)
E.g.f.: (1/2)*((1+2*x)*cos(x)-cosh(x)+sin(x)-sinh(x)). - Stefano Spezia, Aug 13 2019 after Colin Barker
Comments