OFFSET
1,7
COMMENTS
Obtained as the top element of the vector resulting from multiplying the n-th power of the 6 X 6 matrix [[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 3, 6, 4, -5, 1]] with the column vector which contains only 1's.
LINKS
Peter Steinbach, Golden fields: a case for the heptagon, Math. Mag. Vol. 70, No. 1, Feb. 1997, 22-31.
Index entries for linear recurrences with constant coefficients, signature (1,-5,4,6,3,1).
FORMULA
G.f.: x*(8*x^5+5*x^4-x^3-5*x^2-1)/(x^6+3*x^5+6*x^4+4*x^3-5*x^2+x-1). - Colin Barker, Nov 08 2012
MATHEMATICA
M = {{0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {1, 3, 6, 4, -5, 1}}; v[1] = {1, 1, 1, 1, 1, 1}; v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
LinearRecurrence[{1, -5, 4, 6, 3, 1}, {1, 1, 1, 1, 1, 1}, 40] (* Harvey P. Dale, Feb 17 2024 *)
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Roger L. Bagula and Gary W. Adamson, Sep 20 2006
EXTENSIONS
Edited by N. J. A. Sloane, Sep 24 2006
Definition changed using Barker's g.f. by Bruno Berselli, Sep 19 2017
STATUS
approved