A138766 Real part of upper left and lower right terms of [1,(1+I); 1,1]^n * [1,0].

1, 2, 4, 7, 11, 14, 8, -31, -167, -558, -1572, -4025, -9645, -21922, -47536, -98431, -193935, -360094, -617100, -929593, -1056037, -145682, 4258520, 18546401, 58207561, 158790322, 398072524, 938582407, 2103831971, 4502207934

Offset

1,2

Comments

The sequence exhibits curious strings of (-) signs.

Links

Table of n, a(n) for n=1..30.

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

Sequence in context: A177754 A086795 A064690 * A192638 A211372 A054850

Adjacent sequences: A138763 A138764 A138765 * A138767 A138768 A138769

Keyword

sign,easy

Author

Gary W. Adamson, Mar 30 2008

Status

approved