A249577 List of triples (r,s,t): the matrix M = [[1,4,4][1,3,2][1,2,1]] is raised to successive negative powers, then (r,s,t) are the square roots of M[3,1], M[1,1], M[1,3] respectively.

2, -1, 1, -4, 3, -2, 10, -7, 5, -24, 17, -12, 58, -41, 29, -140, 99, -70, 338, -239, 169, -816, 577, -408, 1970, -1393, 985, -4756, 3363, -2378, 11482, -8119, 5741, -27720, 19601, -13860, 66922, -47321, 33461, -161564, 114243, -80782, 390050, -275807, 195025, -941664, 665857, -470832

Offset: 0

Author

Russell Walsmith, Nov 01 2014

Keywords

• sign
• tabf
• easy

Comments

The sequence comprises, in reverse order, numbers to the right of a(0) in A249576.

Examples

			M^-1 = [[1,-4,4][-1,3,-2][1,-2,1]]. sqrt(M[1,3]) = 2; M[3,3] = M[1,1] = -1; M[3,1] = 1. Hence a(0) = 2; a(1) = -1; a(2) = 1.
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,-2,0,0,1).

Crossrefs

Cf. A249576, A000129, A001333, A163271, A077985.

Programs

Mathematica

LinearRecurrence[{0,0,-2,0,0,1},{2,-1,1,-4,3,-2},50] (* Harvey P. Dale, Aug 02 2024 *)

PARI

Vec(-(x^4+x^2-x+2)/(x^6-2*x^3-1) + O(x^100)) \\ Colin Barker, Nov 02 2014

Formula

a(n) = -2*a(n-3)+a(n-6); G.f.: -(x^4+x^2-x+2) / (x^6-2*x^3-1). - Colin Barker, Nov 02 2014