|
%I #17 Sep 08 2022 08:46:05
%S 0,24,384,2064,7104,18984,43008,86688,160128,276408,451968,706992,
%T 1065792,1557192,2214912,3077952,4190976,5604696,7376256,9569616,
%U 12255936,15513960,19430400,24100320,29627520,36124920,43714944,52529904,62712384,74415624,87803904
%N Sequences from the quartic oscillator.
%C There are 50 polynomials from the sequences which can be summed to a solution of the quartic oscillator.
%H Charles A. Lane, <a href="/A228406/a228406.nb">Mathematica code for the polynomial version of the quartic oscillator</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(n) = (n+1)*(n+2)*(n+3)*(4+44*n/5+16*n^2/5).
%F G.f.: 24*x*(1+10*x+5*x^2) / (x-1)^6. - _R. J. Mathar_, Oct 24 2013
%F a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - _Wesley Ivan Hurt_, Oct 24 2014
%p A228406:=n->(n+1)*(n+2)*(n+3)*(4+44*n/5+16*n^2/5): seq(A228406(n), n=-1..30); # _Wesley Ivan Hurt_, Oct 24 2014
%t CoefficientList[Series[24*x*(1 + 10*x + 5*x^2)/(x - 1)^6, {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Oct 24 2014 *)
%o (Magma) [(n+1)*(n+2)*(n+3)*(4+44*n/5+16*n^2/5) : n in [-1..30]]; // _Wesley Ivan Hurt_, Oct 24 2014
%Y Cf. A225007.
%K nonn,easy
%O -1,2
%A _Charles A. Lane_, Aug 22 2013
|
