A092414 Negative of the determinant of the 3 X 3 matrix with entries (X+Y)^n.

0, 0, 8, 2016, 301856, 35402880, 3596797568, 332433378816, 28736957620736, 2363831961200640, 187161691763222528, 14378930653933756416, 1078142718948065878016, 79242945178480535961600

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Index entries for linear recurrences with constant coefficients, signature (276,-30380,1667088,-45607680,497664000).

Formula

a(n) = 50^n + 54^n - 48^n + 64^n - 2*60^n.

G.f.: 8*x^2*(1440*x^2+24*x-1) / ((48*x-1)*(50*x-1)*(54*x-1)*(60*x-1)*(64*x-1)). [Colin Barker, Dec 13 2012]

a(0)=0, a(1)=0, a(2)=8, a(3)=2016, a(4)=301856, a(n)=276*a(n-1)- 30380*a(n-2)+ 1667088*a(n-3)-45607680*a(n-4)+497664000*a(n-5). - Harvey P. Dale, Dec 31 2012

Example

n=3 gives
[2^3, 3^3, 4^3]
[3^3, 4^3, 5^3]
[4^3, 5^3, 6^3]
=
[8,27,64]
[27,64,125]
[64,125,216]
with det -2016

Mathematica

Table[Abs[Det[Table[x+n, {x, 2, 4}, {n, 0, 2}]^i]], {i, 0, 15}] (* or *) LinearRecurrence[ {276, -30380, 1667088, -45607680, 497664000}, {0, 0, 8, 2016, 301856}, 20] (* Harvey P. Dale, Dec 31 2012 *)

Prog

(PARI) for(j=0, 15, m=matrix(3, 3, X, Y, (X+Y)^j); print1(", "-matdet(m)))

Crossrefs

Sequence in context: A076955 A362292 A024112 * A295217 A297950 A298559

Adjacent sequences: A092411 A092412 A092413 * A092415 A092416 A092417

Keyword

nonn,easy

Author

Jon Perry, Mar 22 2004

Status

approved