A188653 - OEIS

%I #27 Jul 08 2023 18:43:25

%S 1,1,-3,7,-11,17,-23,31,-39,49,-59,71,-83,97,-111,127,-143,161,-179,

%T 199,-219,241,-263,287,-311,337,-363,391,-419,449,-479,511,-543,577,

%U -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

%N Second differences of A000463; first differences of A188652.

%H Reinhard Zumkeller, <a href="/A188653/b188653.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-2,0,2,1).

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

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

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

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

%F G.f.: x*(-1-3*x+x^2+x^3) / ((x-1)*(1+x)^3). - _R. J. Mathar_, Apr 14 2011

%F a(n) = a(-n) = ((2*n^2-5)*(-1)^n+1)/4. - _Bruno Berselli_, Sep 14 2011

%F E.g.f.: 1 + ((x^2 - x - 2)*cosh(x) - (x^2 - x - 3)*sinh(x))/2. - _Stefano Spezia_, Jul 08 2023

%t LinearRecurrence[{-2, 0, 2, 1}, {1, 1, -3, 7}, 75] (* _Jean-François Alcover_, Dec 16 2021 *)

%o (Haskell)

%o a188653 n = a188653_list !! (n-1)

%o a188653_list = zipWith (-) (tail a188652_list) a188652_list

%Y Cf. A056220, A142463, A047838.

%Y Cf. A000463, A188652.

%K sign,easy

%O 1,3

%A _Reinhard Zumkeller_, Apr 13 2011