A110294 a(2*n) = A028230(n), a(2*n+1) = -A067900(n+1).
1, -8, 15, -112, 209, -1560, 2911, -21728, 40545, -302632, 564719, -4215120, 7865521, -58709048, 109552575, -817711552, 1525870529, -11389252680, 21252634831, -158631825968, 296011017105, -2209456310872, 4122901604639, -30773756526240, 57424611447841
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (0,14,0,-1).
Programs
-
Magma
[(3*(-1)^n-1)*Evaluate(ChebyshevSecond(n+1), 2)/2: n in [0..40]]; // G. C. Greubel, Jan 04 2023
-
Maple
seriestolist(series((1-8*x+x^2)/((x^2-4*x+1)*(x^2+4*x+1)), x=0,25));
-
Mathematica
CoefficientList[Series[(1-8x+x^2)/((1-4x+x^2)(1+4x+x^2)), {x, 0, 24}], x] (* Michael De Vlieger, Nov 01 2016 *) LinearRecurrence[{0,14,0,-1},{1,-8,15,-112},30] (* Harvey P. Dale, Dec 16 2024 *) -
PARI
Vec((1-8*x+x^2)/((1-4*x+x^2)*(1+4*x+x^2)) + O(x^30)) \\ Colin Barker, Nov 01 2016
-
SageMath
[(3*(-1)^n-1)*chebyshev_U(n,2)/2 for n in range(41)] # G. C. Greubel, Jan 04 2023
Formula
G.f.: (1-8*x+x^2) / ((1-4*x+x^2)*(1+4*x+x^2)).
a(n) = 14*a(n-2) - a(n-4) for n>3. - Colin Barker, Nov 01 2016
a(n) = (3*(-1)^n - 1)*A001353(n+1)/2. - R. J. Mathar, Sep 11 2019
Comments