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A228406 Sequences from the quartic oscillator. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 21 05:31 EDT 2019. Contains 326162 sequences. (Running on oeis4.)