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 A092414 Negative of the determinant of the 3 X 3 matrix with entries (X+Y)^n. 0
 0, 0, 8, 2016, 301856, 35402880, 3596797568, 332433378816, 28736957620736, 2363831961200640, 187161691763222528, 14378930653933756416, 1078142718948065878016, 79242945178480535961600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Index entries for linear recurrences with constant coefficients, signature (276,-30380,1667088,-45607680,497664000). FORMULA 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: A303253 A076955 A024112 * A295217 A297950 A298559 Adjacent sequences:  A092411 A092412 A092413 * A092415 A092416 A092417 KEYWORD nonn,easy AUTHOR Jon Perry, Mar 22 2004 STATUS approved

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Last modified May 21 15:36 EDT 2022. Contains 353921 sequences. (Running on oeis4.)