A116953 a(n) = Floor[1/2((1-2/Sqrt[3])^n+(1-2/Sqrt[3])^n)]

1, 1, 2, 5, 10, 23, 50, 107, 232, 500, 1078, 2323, 5007, 10789, 23248, 50092, 107934, 232566, 501111, 1079745, 2326528, 5012972, 10801454, 23273900, 50148285, 108054537

Offset

0,3

Comments

A Binet sequence solution with ratio =(2+Sqrt[3])/Sqrt[3] ( called a trident sequence after the graphic it comes from).

Links

Table of n, a(n) for n=0..25.

Mathematica

Needs["DiscreteMath`RSolve`"]; Clear[f]; f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == 2*a[n - 1] + a[n - 2]/3, a[0] == 1, a[1] == 1}, a[n], n][[1]] // Simplify] // ToRadicals Table[Floor[N[f[n]]], {n, 0, 25}]

Crossrefs

Sequence in context: A260744 A317535 A087640 * A099516 A293741 A291559

Adjacent sequences: A116950 A116951 A116952 * A116954 A116955 A116956

Keyword

nonn

Author

Roger L. Bagula, Apr 03 2006

Extensions

Edited by N. J. A. Sloane, May 04 2006

Status

approved