OFFSET
1,2
LINKS
P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31.
Index entries for linear recurrences with constant coefficients, signature (11,4,-1).
FORMULA
a(n) = 11a(n-1)+4a(n-2)-a(n-3), a(0)=1, a(1)=14, a(2)=157 (derived from the minimal polynomial of the matrix M).
G.f.: -x*(x^2-3*x-1) / (x^3-4*x^2-11*x+1). [Colin Barker, Dec 07 2012]
MAPLE
a[0]:=1: a[1]:=14: a[2]:=157: for n from 3 to 20 do a[n]:=11*a[n-1]+4*a[n-2]-a[n-3] od: seq(a[n], n=0..20);
MATHEMATICA
M = {{6, 5, 3}, {5, 4, 2}, {3, 2, 1}}; v[1] = {1, 1, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]
LinearRecurrence[{11, 4, -1}, {1, 14, 157}, 30] (* Harvey P. Dale, Oct 18 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson and Roger L. Bagula, Oct 17 2006
EXTENSIONS
Edited by N. J. A. Sloane, Oct 29 2006
STATUS
approved