A188653 Second differences of A000463; first differences of A188652.

1, 1, -3, 7, -11, 17, -23, 31, -39, 49, -59, 71, -83, 97, -111, 127, -143, 161, -179, 199, -219, 241, -263, 287, -311, 337, -363, 391, -419, 449, -479, 511, -543, 577, -611, 647, -683, 721, -759, 799, -839, 881, -923, 967, -1011, 1057, -1103, 1151, -1199, 1249, -1299, 1351, -1403, 1457, -1511, 1567, -1623, 1681, -1739, 1799, -1859, 1921, -1983, 2047, -2111, 2177, -2243, 2311, -2379, 2449, -2519, 2591, -2663, 2737, -2811

Offset

1,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (-2,0,2,1).

Formula

a(2*n) = a(2*n-1)+4*n^2-2*n-2, a(2*n+1) = -a(2*n)-2*n.

a(2*n) = A056220(n), a(2*n-1) = -A142463(n).

Abs(a(n)) = A047838(n) for n > 1.

a(n) = A188652(n+1)-A188652(n) = A000463(n+2)-2*A000463(n+1)+A000463(n).

G.f.: x*(-1-3*x+x^2+x^3) / ((x-1)*(1+x)^3). - R. J. Mathar, Apr 14 2011

a(n) = a(-n) = ((2*n^2-5)*(-1)^n+1)/4. - Bruno Berselli, Sep 14 2011

E.g.f.: 1 + ((x^2 - x - 2)*cosh(x) - (x^2 - x - 3)*sinh(x))/2. - Stefano Spezia, Jul 08 2023

Mathematica

LinearRecurrence[{-2, 0, 2, 1}, {1, 1, -3, 7}, 75] (* Jean-François Alcover, Dec 16 2021 *)

Prog

(Haskell)
a188653 n = a188653_list !! (n-1)
a188653_list = zipWith (-) (tail a188652_list) a188652_list

Crossrefs

Cf. A056220, A142463, A047838.

Cf. A000463, A188652.

Sequence in context: A237662 A134707 A047838 * A333996 A262502 A211076

Adjacent sequences: A188650 A188651 A188652 * A188654 A188655 A188656

Keyword

sign,easy

Author

Reinhard Zumkeller, Apr 13 2011

Status

approved