OFFSET
1,2
COMMENTS
The sequence exhibits curious strings of (-) signs.
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-4,0,-1).
FORMULA
Real part of terms (1,1) and (2,2) of matrix [1,(1+I); 1,1]^n * [1,0]; I^2 = -1.
a(n) = 4*a(n-1)-4*a(n-2)-a(n-4). G.f.: -x*(x^3+2*x-1) / (x^4+4*x^2-4*x+1). - Colin Barker, Oct 20 2013
EXAMPLE
a(5) = 11 since fifth power of the matrix generator = [(11,20),(3,27); (15,12),(11,20)]; where (11,20) = (11 + 20*I).
MATHEMATICA
LinearRecurrence[{4, -4, 0, -1}, {1, 2, 4, 7}, 40] (* Harvey P. Dale, May 13 2017 *)
PROG
(PARI) Vec(-x*(x^3+2*x-1)/(x^4+4*x^2-4*x+1) + O(x^100)) \\ Colin Barker, Oct 20 2013
(PARI) a(n) = real([1, (1+I); 1, 1]^n * [1, 0]~)[1] \\ Colin Barker, Oct 20 2013
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Gary W. Adamson, Mar 30 2008
STATUS
approved