A227200 a(n) = a(n-1) + a(n-2) - 2^(n-1) with a(0)=a(2)=0, a(1)=-a(3)=1, a(4)=-5.
0, 1, 0, -1, -5, -14, -35, -81, -180, -389, -825, -1726, -3575, -7349, -15020, -30561, -61965, -125294, -252795, -509161, -1024100, -2057549, -4130225, -8284926, -16609455, -33282989, -66669660, -133507081, -267285605, -535010414, -1070731475
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- C. N. Phadte and S. P. Pethe, On Second Order Non-homogeneous recurrence relation, Annales Mathematicae et informaticae, 41 (2013), pp. 205-210.
- Index entries for linear recurrences with constant coefficients, signature (3,-1,-2).
Programs
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BASIC
LET N=0 LET L=0 LET M=1 PRINT L PRINT M FOR I=1 TO 30 LET N=M+L-(2)^(I-1) PRINT N LET L=M LET M=N NEXT I END
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Magma
m:=30; R
:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!((1-3*x)/((1-2*x)*(1-x-x^2)))); // Bruno Berselli, Oct 03 2013 -
Magma
I:=[0,1,0,-1,-5]; [n le 5 select I[n] else Self(n-1)+Self(n-2)-2^(n-3): n in [1..35]]; // Vincenzo Librandi, Oct 05 2013
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Mathematica
Table[LucasL[n + 1] - 2^n, {n, 0, 30}] (* Bruno Berselli, Oct 03 2013 *) CoefficientList[Series[x (1 - 3 x)/((1 - 2 x) (1 - x - x^2)), {x, 0, 40}], x](* Vincenzo Librandi, Oct 05 2013 *) -
PARI
a(n)=fibonacci(n)+fibonacci(n+2)-2^n \\ Charles R Greathouse IV, Oct 03 2013
Formula
G.f.: x*(1-3*x)/((1-2*x)*(1-x-x^2)).
a(n) = 3*a(n-1) -a(n-2) -2*a(n-3). [Bruno Berselli, Oct 03 2013]
Extensions
More terms from Bruno Berselli, Oct 03 2013
Comments