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Definition uses New name using the g.f. of _from _Colin Barker_, May 30 2016
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Definition uses the g.f. of _Colin Barker._, May 30 2016
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<a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2, -3, 4, -3, 2, -1).
Starting with 0, 1, 2, 3, ... (A001477), write 0, 0 instead of a(0), 1, 1 instead of a(3) and in general n, n instead of a(3n).
Expansion of x^2*(1+x)*(1-x+x^2) / ((1-x)^2*(1+x^2)^2).
Old definition was: "Starting with 0, 1, 2, 3, ... (A001477), write 0, 0 instead of a(0), 1, 1 instead of a(3) and in general n, n instead of a(3n)".
a(n) = (-2+(-i)^n+i^n+(4-(1+i)*(-i)^n-(1-i)*i^n)*n)/8 where i = sqrt(-1).
a(n) = 2*a(n-1)-3*a(n-2)+4*a(n-3)-3*a(n-4)+2*a(n-5)-a(n-6) for n>5.
a(n) = (-2+(-i)^n+i^n+(4-(1+i)*(-i)^n-(1-i)*i^n)*n)/8 where i = sqrt(-1).
a(n) = 2*a(n-1)-3*a(n-2)+4*a(n-3)-3*a(n-4)+2*a(n-5)-a(n-6) for n>5. (End)
Definition uses the g.f. of Colin Barker.
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From Colin Barker, May 30 2016: (Start)
a(n) = (-2+(-i)^n+i^n+(4-(1+i)*(-i)^n-(1-i)*i^n)*n)/8 where i = sqrt(-1).
a(n) = 2*a(n-1)-3*a(n-2)+4*a(n-3)-3*a(n-4)+2*a(n-5)-a(n-6) for n>5.
G.f.: x^2*(1+x)*(1-x+x^2) / ((1-x)^2*(1+x^2)^2).
(End)
(PARI) concat(vector(2), Vec(x^2*(1+x)*(1-x+x^2)/((1-x)^2*(1+x^2)^2) + O(x^50))) \\ Colin Barker, May 30 2016
nonn,changed,easy
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