A144462 A triangle sequence designed as a step function around the determinants: a(n)=A000045(n); t(n,m)=If[m == 0 || m == 1, 2 - m, If[ m < n, Ceiling[(a(m) - 1)/a(n) + 1], a(n) + 1]].

2, 2, 1, 2, 1, 2, 2, 1, 1, 3, 2, 1, 1, 2, 4, 2, 1, 1, 2, 2, 6, 2, 1, 1, 2, 2, 2, 9, 2, 1, 1, 2, 2, 2, 2, 14, 2, 1, 1, 2, 2, 2, 2, 2, 22, 2, 1, 1, 2, 2, 2, 2, 2, 2, 35, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 56

Offset

1,1

Comments

Row sums: {2, 3, 5, 7, 10, 14, 19, 26, 36, 51, 74}.

Links

Table of n, a(n) for n=1..66.

Formula

a(n)=A000045(n); t(n,m)=If[m == 0 || m == 1, 2 - m, If[ m < n, Ceiling[(a(m) - 1)/a(n) + 1], a(n) + 1]].

Example

{2},
{2, 1},
{2, 1, 2},
{2, 1, 1, 3},
{2, 1, 1, 2, 4},
{2, 1, 1, 2, 2, 6},
{2, 1, 1, 2, 2, 2, 9},
{2, 1, 1, 2, 2, 2, 2, 14},
{2, 1, 1, 2, 2, 2, 2, 2, 22},
{2, 1, 1, 2, 2, 2, 2, 2, 2, 35},
{2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 56}

Mathematica

Clear[a, b, t, n, m]; a[n_] := Fibonacci[n]; t[n_, m_] := If[m == 0 || m == 1, 2 - m, If[ m < n, Ceiling[(a[m] - 1)/a[n] + 1], a[n] + 1]]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

Crossrefs

Cf. A000045.

Sequence in context: A264032 A366597 A251138 * A370559 A378301 A112104

Adjacent sequences: A144459 A144460 A144461 * A144463 A144464 A144465

Keyword

nonn,uned

Author

Roger L. Bagula and Gary W. Adamson, Oct 08 2008

Status

approved