A115634 - OEIS

%I #19 Dec 06 2024 17:59:52

%S 1,0,-3,0,-3,0,-3,0,-3,0,-3,0,-3,0,-3,0,-3,0,-3,0,-3,0,-3,0,-3,0,-3,0,

%T -3,0,-3,0,-3,0,-3,0,-3,0,-3,0,-3,0,-3,0,-3,0,-3,0,-3,0,-3,0,-3,0,-3,

%U 0,-3,0,-3,0

%N Expansion of (1-4*x^2)/(1-x^2).

%C Row sums of number triangle A115633.

%H G. C. Greubel, <a href="/A115634/b115634.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).

%F a(n) = 4*0^n - 3*(1 + (-1)^n)/2.

%F a(n) = Sum_{k=0..n} A115633(n, k).

%F From _G. C. Greubel_, Nov 23 2021: (Start)

%F a(n) = 1 if n = 0, otherwise a(n) = -A010674(n-1).

%F E.g.f.: 4 - 3*cosh(x). (End)

%t Join[{1}, -3*Mod[Range[100] -1, 2]] (* _G. C. Greubel_, Nov 23 2021 *)

%t CoefficientList[Series[(1-4x^2)/(1-x^2),{x,0,100}],x] (* or *) LinearRecurrence[{0,1},{1,0,-3},100] (* or *) PadRight[{1},100,{-3,0}] (* _Harvey P. Dale_, Dec 06 2024 *)

%o (Magma) [4*0^n -3*(1+(-1)^n)/2: n in [0..100]]; // _G. C. Greubel_, Nov 23 2021

%o (Sage) [1]+[-3*((n-1)%2) for n in (1..100)] # _G. C. Greubel_, Nov 23 2021

%Y Cf. A010674, A115633.

%K easy,sign

%O 0,3

%A _Paul Barry_, Jan 27 2006