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 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, 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 21 22:27 EDT 2024. Contains 374478 sequences. (Running on oeis4.)