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 A123972 a(n) = n^3 - n^2 - 2*n + 1. 3
 1, -1, 1, 13, 41, 91, 169, 281, 433, 631, 881, 1189, 1561, 2003, 2521, 3121, 3809, 4591, 5473, 6461, 7561, 8779, 10121, 11593, 13201, 14951, 16849, 18901, 21113, 23491, 26041, 28769, 31681, 34783, 38081, 41581, 45289, 49211, 53353, 57721, 62321, 67159, 72241 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n) is the determinant of the 3 X 3 matrix {{n,-1,0 },{-1,n,-1},{0,-1,n-1}}. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = (n + 2*cos(2*Pi/7)) * (n + 2*cos(4*Pi/7)) * (n + 2*cos(6*Pi/7)). Cf. 3rd column from the left in the array of A162997. - Gary W. Adamson, Jul 23 2009 a(n), n>2 equals lower right term in M^3, M is the 2 X 2 matrix {{1,(n-2)}{1,(n-1}}. - Gary W. Adamson, Jun 29 2011 Starting (1, 13, 41, ...) = the binomial transform of (1, 12, 16, 6). - Gary W. Adamson, Jun 29 2011 G.f.: (1 - 5*x + 11*x^2 - x^3)/(1-x)^4. - Colin Barker, Jan 29 2012 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 27 2012 MAPLE with(linalg): M:=n->matrix(3, 3, [n, -1, 0, -1, n, -1, 0, -1, n-1]): seq(det(M(n)), n=0..42); MATHEMATICA CoefficientList[Series[(1-5*x+11*x^2-x^3)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 27 2012 *) PROG (PARI) a(n)=n^3-n^2-2*n+1 \\ Charles R Greathouse IV, Jun 30 2011 (Magma) I:=[1, -1, 1, 13]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 27 2012 CROSSREFS Cf. A162997. Sequence in context: A102083 A139866 A026918 * A167585 A141970 A305155 Adjacent sequences: A123969 A123970 A123971 * A123973 A123974 A123975 KEYWORD sign,easy AUTHOR Gary W. Adamson and Roger L. Bagula, Oct 30 2006 EXTENSIONS Edited by N. J. A. Sloane, Nov 01 2006 and Nov 24 2006 STATUS approved

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Last modified February 21 07:54 EST 2024. Contains 370219 sequences. (Running on oeis4.)