A085422 A sequence analogous to the Lucas numbers (A000032), with ratios converging to Pi.

-1, 2, 4, 13, 40, 125, 392, 1231, 3867, 12148, 38164, 119895, 376661, 1183315, 3717493, 11678848, 36690183, 115265609, 362117590, 1137625960, 3573957358, 11227918180, 35273545269, 110815110683, 348135937628, 1093701304102

Offset: 0

Author

Gary W. Adamson, Jun 29 2003

Keywords

• sign
• easy

Comments

The Lucas numbers have 1 = phi - 1/phi where this sequence has k and the ratios of the Lucas numbers converge to phi.

Examples

			a(5) = floor[(Pi - 1/Pi)*40+13] = 125.
		

Crossrefs

Cf. A000032.

Formula

a(0) = -1, a(1) = 2, a(n+2) = floor[k*a(n+1)+a(n)], where k = Pi - 1/Pi = 2.82328276....

Lim(n->inf) a(n)/a(n-1) = Pi.

Extensions

Edited and extended by David Wasserman, Feb 01 2005