A228406 Sequences from the quartic oscillator.

0, 24, 384, 2064, 7104, 18984, 43008, 86688, 160128, 276408, 451968, 706992, 1065792, 1557192, 2214912, 3077952, 4190976, 5604696, 7376256, 9569616, 12255936, 15513960, 19430400, 24100320, 29627520, 36124920, 43714944, 52529904, 62712384, 74415624, 87803904

Offset

-1,2

Comments

There are 50 polynomials from the sequences which can be summed to a solution of the quartic oscillator.

Links

Table of n, a(n) for n=-1..29.

Charles A. Lane, Mathematica code for the polynomial version of the quartic oscillator

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(n) = (n+1)*(n+2)*(n+3)*(4+44*n/5+16*n^2/5).

G.f.: 24*x*(1+10*x+5*x^2) / (x-1)^6. - R. J. Mathar, Oct 24 2013

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

Maple

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

Mathematica

CoefficientList[Series[24*x*(1 + 10*x + 5*x^2)/(x - 1)^6, {x, 0, 30}], x] (* Wesley Ivan Hurt, Oct 24 2014 *)

Prog

(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

Crossrefs

Cf. A225007.

Sequence in context: A022565 A025974 A059157 * A087292 A081138 A269181

Adjacent sequences: A228403 A228404 A228405 * A228407 A228408 A228409

Keyword

nonn,easy

Author

Charles A. Lane, Aug 22 2013

Status

approved