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A114568
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a(n) = 4694*a(n-2) + 9380*a(n-3) for n >= 3 with a(0) = 0 and a(1) = a(2) = 1.
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0
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0, 1, 1, 4694, 14074, 22043016, 110093076, 103601931224, 723540388824, 487340138218336, 4368084700020976, 2294361417644038304, 25075040078386453024, 10810705128907312553856, 139223348225447089786176, 50980653751026190057165184, 754918810679399231211479424
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OFFSET
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0,4
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LINKS
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Table of n, a(n) for n=0..16.
Index entries for linear recurrences with constant coefficients, signature (0,4694,9380).
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FORMULA
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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)
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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Sequence in context: A204073 A256808 A114542 * A251135 A237699 A235022
Adjacent sequences: A114565 A114566 A114567 * A114569 A114570 A114571
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KEYWORD
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nonn,less,easy
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AUTHOR
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Roger L. Bagula, Feb 16 2006
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EXTENSIONS
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More terms from Colin Barker, Jan 21 2013
Edited and new name using formula from Colin Barker, Joerg Arndt, Nov 21 2019
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STATUS
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approved
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