A097576 A 2 X 2 matrix version of A005185: Hofstadter's sequence.

0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 3, 3, 3, 6, 3, 3, 3, 6, 4, 4, 4, 8, 5, 5, 5, 10, 5, 5, 5, 10, 6, 6, 6, 12, 6, 6, 6, 12, 6, 6, 6, 12, 8, 8, 8, 16, 8, 8, 8, 16, 8, 8, 8, 16, 10, 10, 10, 20, 9, 9, 9, 18, 10, 10, 10, 20, 11, 11, 11, 22, 11, 11, 11, 22, 12, 12, 12, 24, 12, 12, 12, 24, 12, 12, 12

Offset

0,8

Links

Table of n, a(n) for n=0..86.

Formula

A[n_]:=A[n]=A[n-A[n-1][[1, 1]]]+A[n-A[n-2][[1, 2]]]; A[0]:={{0, 1}, {1, 1}}; A[1]:={{1, 1}, {1, 2}};

Mathematica

Clear[A, M] (* Hofstadter 2 X 2 Matrix sequence*) (* by Roger L. Bagula *) digits=100 A[n_]:=A[n]=A[n-A[n-1][[1, 1]]]+A[n-A[n-2][[1, 2]]]; A[0]:={{0, 1}, {1, 1}}; A[1]:={{1, 1}, {1, 2}}; (* flattened sequence of 2 X 2 matrices made with a Hofstadter recurrence*) b=Flatten[Table[A[n], {n, 0, digits}]] ListPlot[b, PlotJoined->True]

Crossrefs

Cf. A005185.

Sequence in context: A023153 A023159 A098983 * A029250 A341584 A110884

Adjacent sequences: A097573 A097574 A097575 * A097577 A097578 A097579

Keyword

nonn

Author

Roger L. Bagula, Aug 28 2004

Status

approved