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A181829 a(n) = 4*A060819(n-2)*A060819(n+2). 2
0, -12, -4, -12, 0, 20, 12, 84, 8, 180, 60, 308, 24, 468, 140, 660, 48, 884, 252, 1140, 80, 1428, 396, 1748, 120, 2100, 572, 2484, 168, 2900, 780, 3348, 224, 3828, 1020, 4340, 288, 4884, 1292, 5460, 360, 6068, 1596 (list; graph; refs; listen; history; text; internal format)
OFFSET

-2,2

COMMENTS

A060819 is sign extended to negative n by A060819(0)=0 and A060819(-n) = -A060819(n).

LINKS

G. C. Greubel, Table of n, a(n) for n = -2..5000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).

FORMULA

a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12). This implies that A033996, A158443 and two other 2nd-order polynomials are quadrisections. - R. J. Mathar, Feb 01 2011

From G. C. Greubel, Sep 20 2018: (Start)

a(n) = (1/16)*(n^2 - 4)*(37 - 27*(-1)^n + 6*cos((n*Pi)/2)).

G.f.: 4*(-3 - x - 3*x^2 + 14*x^4 + 6*x^5 + 30*x^6 + 2*x^7 + 21*x^8 + 3*x^9 + 5*x^10)/(x*(1 - x^4)^3).

E.g.f.: (1/8)*((5*x^2 + 32*x - 20)*cosh(x) + (32*x^2 + 5*x - 128)*sinh(x) -3*(x^2 + 4)*cos(x) -3*x*sin(x)). (End)

MATHEMATICA

Table[(1/16)*(n^2-4)*(37-27*(-1)^n +6*Cos[(n*Pi)/2]), {n, -2, 50}] (* G. C. Greubel, Sep 20 2018 *)

LinearRecurrence[{0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1}, {0, -12, -4, -12, 0, 20, 12, 84, 8, 180, 60, 308}, 50] (* Harvey P. Dale, Jan 08 2019 *)

PROG

(PARI) for(n=-2, 50, print1((1/16)*(n^2-4)*(37-27*(-1)^n+6*cos((n*Pi)/2), ", ")) \\ G. C. Greubel, Sep 20 2018

(MAGMA) R:= RealField(20); [(1/16)*Round((n^2-4)*(37-27*(-1)^n+ 6*Cos((n*Pi(R))/2))): n in [-2..50]]; // G. C. Greubel, Sep 20 2018

CROSSREFS

Cf. A180082.

Sequence in context: A004477 A328285 A307164 * A199693 A166206 A040137

Adjacent sequences:  A181826 A181827 A181828 * A181830 A181831 A181832

KEYWORD

sign,easy,less

AUTHOR

Paul Curtz, Nov 13 2010

STATUS

approved

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Last modified May 26 01:22 EDT 2020. Contains 334613 sequences. (Running on oeis4.)