A233828 a(n) = 2*a(n-1) + 2*a(n-2) + a(n-3). a(0) = -1, a(1) = 1, a(2) = 1.
-1, 1, 1, 3, 9, 25, 71, 201, 569, 1611, 4561, 12913, 36559, 103505, 293041, 829651, 2348889, 6650121, 18827671, 53304473, 150914409, 427265435, 1209664161, 3424773601, 9696140959, 27451493281, 77720042081, 220039211683, 622970000809, 1763738467065
Offset: 0
Keywords
Examples
G.f. = -1 + x + x^2 + 3*x^3 + 9*x^4 + 25*x^5 + 71*x^6 + 201*x^7 + 569*x^8 + ...
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2, 2, 1).
Programs
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Magma
m:=50; R
:=PowerSeriesRing(Integers(), m); Coefficients(R!((-1+3*x+x^2)/(1-2*x-2*x^2-x^3))); // G. C. Greubel, Aug 07 2018 -
Mathematica
CoefficientList[Series[(-1+3*x+x^2)/(1-2*x-2*x^2-x^3), {x, 0, 50}], x] (* G. C. Greubel, Aug 07 2018 *) -
PARI
{a(n) = if( n<0, polcoeff( (-1 -x + x^2) / (1 + 2*x + 2*x^2 - x^3) + x * O(x^-n), -n), polcoeff( (-1 + 3*x + x^2) / (1 - 2*x - 2*x^2 - x^3) + x * O(x^n), n))}