A157517 - OEIS

%I #11 Sep 08 2022 08:45:42

%S 7,13,7,-11,-41,-83,-137,-203,-281,-371,-473,-587,-713,-851,-1001,

%T -1163,-1337,-1523,-1721,-1931,-2153,-2387,-2633,-2891,-3161,-3443,

%U -3737,-4043,-4361,-4691,-5033,-5387,-5753,-6131,-6521,-6923,-7337,-7763,-8201,-8651

%N a(n) = 7 + 12*n - 6*n^2.

%C From John Couch Adams multisteps integration of differential equations, 1855.

%D P. Curtz Integration numerique des systemes differentiels, C.C.S.A., Arcueil, 1969, p. 36.

%H Vincenzo Librandi, <a href="/A157517/b157517.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 12*n + 6 - A140811(n) = A017593(n) - A140811(n).

%F Recurrences: a(n) = 2*a(n-1) - a(n-2) - 12 = 3*a(n-1) - 3*a(n-2) + a(n-3).

%F First differences: a(n+1) - a(n) = -A017593(n-1), n > 0. Second differences are all -12.

%F a(n+2) - a(n) = -A008606(n).

%F G.f.: (-7 + 8*x + 11*x^2)/(x-1)^3. - _R. J. Mathar_, Mar 15 2009

%o (Magma) [7+12*n-6*n^2: n in [0..50]]; // _Vincenzo Librandi_, Aug 07 2011

%o (PARI) a(n)=7+12*n-6*n^2 \\ _Charles R Greathouse IV_, Jun 17 2017

%K sign,easy

%O 0,1

%A _Paul Curtz_, Mar 02 2009

%E Edited and extended by _R. J. Mathar_, Mar 15 2009