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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
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
KEYWORD
sign,easy
AUTHOR
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.)