A103610 4 X infinity array read by rows: let M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 1, 0}}, w[0] = {0, 0, 1, 1}', w[n]' = M*w[n -1]'; the n-th row of the array is w[n]' (the prime denotes transpose).

0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 3, 2, 2, 3, 3, 2, 3, 3, 5, 3, 3, 5, 5, 3, 5, 5, 8, 5, 5, 8, 8, 5, 8, 8, 13, 8, 8, 13, 13, 8, 13, 13, 21, 13, 13, 21, 21, 13, 21, 21, 34, 21, 21, 34, 34, 21, 34, 34, 55, 34, 34, 55, 55, 34, 55, 55, 89, 55, 55, 89, 89, 55, 89

Offset

0,16

Links

Table of n, a(n) for n=0..85.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1).

Formula

From Chai Wah Wu, Sep 05 2023: (Start)

a(n) = a(n-8) + a(n-16) for n > 15.

G.f.: x^2*(-x^13 - x^10 - x^7 - x^6 - x^5 - x^4 - x^3 - x - 1)/(x^16 + x^8 - 1). (End)

Mathematica

M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 1, 0}} w[0] = {0, 0, 1, 1} w[n_] := w[n] = M.w[n - 1] a = Flatten[Table[w[n], {n, 0, Floor[200/4]}]] (* polynomial*) Det[M - x*IdentityMatrix[4]] Solve[Det[M - x*IdentityMatrix[4]] == 0, x]

Crossrefs

Sequence in context: A360240 A185090 A115268 * A305875 A109705 A352578

Adjacent sequences: A103607 A103608 A103609 * A103611 A103612 A103613

Keyword

nonn,tabf

Author

Roger L. Bagula, Mar 24 2005

Extensions

Edited by N. J. A. Sloane, Sep 24 2006

Status

approved