A124026 Let M = {{0, -1, 2}, {-1, 2, -1}, {2, -1, 0}}; v[1] = {0, 0, 1}; v[n] = M.v[n - 1]; then a(n) = v[n][[1]]

0, 2, 1, 14, 26, 132, 364, 1416, 4488, 16016, 53296, 184736, 625184, 2145600, 7303360, 24979584, 85196928, 291057920, 993379072, 3392317952, 11580678656, 39541748736, 134998297600, 460924372992, 1573671536640, 5372896120832

Offset

1,2

Links

Table of n, a(n) for n=1..26.

Index entries for linear recurrences with constant coefficients, signature (2,6,-4).

Formula

a(n) = 2*a(n-1)+6*a(n-2)-4*a(n-3). G.f.: -x^2*(3*x-2)/((2*x+1)*(2*x^2-4*x+1)). [Colin Barker, Nov 08 2012]

Mathematica

M = {{0, -1, 2}, {-1, 2, -1}, {2, -1, 0}}; v[1] = {0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]
LinearRecurrence[{2, 6, -4}, {0, 2, 1}, 40] (* Harvey P. Dale, Jul 18 2015 *)

Crossrefs

Sequence in context: A276851 A080346 A216445 * A106204 A290603 A083074

Adjacent sequences: A124023 A124024 A124025 * A124027 A124028 A124029

Keyword

nonn,easy

Author

Roger L. Bagula and Gary W. Adamson, Oct 31 2006

Extensions

Edited by N. J. A. Sloane, Nov 04 2006

Status

approved