|
%I #31 Feb 18 2022 22:23:36
%S 1,1,1,-1,3,-5,9,-15,25,-41,67,-109,177,-287,465,-753,1219,-1973,3193,
%T -5167,8361,-13529,21891,-35421,57313,-92735,150049,-242785,392835,
%U -635621,1028457,-1664079,2692537,-4356617,7049155,-11405773,18454929
%N Row sums of A128586.
%C Binomial transform of A128587 = A128588: (1, 2, 4, 6, 10, 16, 26, ...).
%H G. C. Greubel, <a href="/A128587/b128587.txt">Table of n, a(n) for n = 1..1000</a>
%H Yüksel Soykan, <a href="https://arxiv.org/abs/1910.03490">Summing Formulas For Generalized Tribonacci Numbers</a>, arXiv:1910.03490 [math.GM], 2019.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-2,0,1).
%F Row sums of triangle A128586, inverse binomial transform of A128588.
%F From _R. J. Mathar_, Jun 03 2009: (Start)
%F a(n) = -2*a(n-1) + a(n-3) = (-1)^n*(1 - A118658(n-1)).
%F G.f.: x*(1+3*x+3*x^2)/((1+x)*(1+x-x^2)). (End)
%F a(n+3) = (-1)^n * A001595(n) for all n>=0. - _M. F. Hasler_ and _Franklin T. Adams-Watters_, Sep 30 2009
%F a(n) = (-1)^(n-1)*(2*Fibonacci(n-2) - 1). - _G. C. Greubel_, Jul 10 2019
%e a(5) = 3 = ( -3, 8, 0, -7, 5).
%t Table[(-1)^(n-1)*(2*Fibonacci[n-2] -1), {n, 40}] (* _G. C. Greubel_, Jul 10 2019 *)
%o (PARI) vector(40, n, f=fibonacci; (-1)^(n-1)*(2*f(n-2)-1)) \\ _G. C. Greubel_, Jul 10 2019
%o (Magma) [(-1)^(n-1)*(2*Fibonacci(n-2)-1): n in [1..40]]; // _G. C. Greubel_, Jul 10 2019
%o (Sage) [(-1)^(n-1)*(2*fibonacci(n-2)-1) for n in (1..40)] # _G. C. Greubel_, Jul 10 2019
%o (GAP) List([1..40], n-> (-1)^(n-1)*(2*Fibonacci(n-2)-1)); # _G. C. Greubel_, Jul 10 2019
%Y Cf. A128586, A128588.
%Y This is a signed version of A001595. - _Franklin T. Adams-Watters_, Sep 30 2009
%Y Cf. A000045.
%K sign
%O 1,5
%A _Gary W. Adamson_, Mar 11 2007
%E More terms from _R. J. Mathar_, Jun 03 2009
%E Duplicate of a formula removed by _R. J. Mathar_, Oct 23 2009
%E Deleted certain dangerous or potentially dangerous links. - _N. J. A. Sloane_, Jan 30 2021
|
