A115634 Expansion of (1-4*x^2)/(1-x^2).

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, -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, 0, -3, 0, -3, 0

Offset: 0

Author

Paul Barry, Jan 27 2006

Keywords

• easy
• sign

Comments

Row sums of number triangle A115633.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (0,1).

Crossrefs

Cf. A010674, A115633.

Programs

Magma

[4*0^n -3*(1+(-1)^n)/2: n in [0..100]]; // G. C. Greubel, Nov 23 2021

Mathematica

Join[{1}, -3*Mod[Range[100] -1, 2]] (* G. C. Greubel, Nov 23 2021 *)
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 *)

Sage

[1]+[-3*((n-1)%2) for n in (1..100)] # G. C. Greubel, Nov 23 2021

Formula

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

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

From G. C. Greubel, Nov 23 2021: (Start)

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

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