A114568 a(n) = 4694*a(n-2) + 9380*a(n-3) for n >= 3 with a(0) = 0 and a(1) = a(2) = 1.

0, 1, 1, 4694, 14074, 22043016, 110093076, 103601931224, 723540388824, 487340138218336, 4368084700020976, 2294361417644038304, 25075040078386453024, 10810705128907312553856, 139223348225447089786176, 50980653751026190057165184, 754918810679399231211479424

Offset

0,4

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (0,4694,9380).

Formula

From Colin Barker, Jan 21 2013: (Start)

a(n) = 4694*a(n-2) + 9380*a(n-3) for n >= 3 with a(0) = 0 and a(1) = a(2) = 1.

G.f.: -x * (x + 1) / ((2*x + 1) * (4690*x^2 + 2*x - 1)). (End)

Maple

with(LinearAlgebra);
M := Matrix([[0, 1, 0], [0, 0, 1], [9380, 4694, 0]]);
w := proc(n) option remember;
     if n = 0 then Matrix([[0], [1], [1]]); elif n >= 1 then
     MatrixMatrixMultiply(M, w(n - 1)); end if;
  end proc;
seq(w(n)[1, 1], n = 0..40); # Petros Hadjicostas, Nov 20 2019

Mathematica

M = {{0, 1, 0}, {0, 0, 1}, {9380, 4694, 0}};
w[0] = {{0}, {1}, {1}};
w[n_] := w[n] = M.w[n - 1];
a = Flatten[Table[w[n][[1]], {n, 0, 25}]]; (* Modified by Petros Hadjicostas, Nov 20 2019 *)
LinearRecurrence[{0, 4694, 9380}, {0, 1, 1}, 20] (* Harvey P. Dale, Apr 11 2020 *)

Crossrefs

Sequence in context: A204073 A256808 A114542 * A251135 A237699 A235022

Adjacent sequences: A114565 A114566 A114567 * A114569 A114570 A114571

Keyword

nonn,less,easy

Author

Roger L. Bagula, Feb 16 2006

Extensions

More terms from Colin Barker, Jan 21 2013

Edited and new name using formula from Colin Barker, Joerg Arndt, Nov 21 2019

Status

approved