A144461 A triangle sequence of determinants: a(n)=A000045(n); t(n,m)=a(m)*(a(n) + 1) - If[ m < n, Round[(a(m) - 1)/a(n) + 1], a(n) + 1]*a(n).

0, 0, 1, 0, 1, 1, -3, 1, 1, 5, -5, 1, 1, 7, 13, -8, 1, 1, 10, 19, 29, -13, 1, 1, 15, 29, 57, 86, -21, 1, 1, 23, 45, 89, 155, 244, -34, 1, 1, 36, 71, 141, 246, 421, 667, -55, 1, 1, 57, 113, 225, 393, 673, 1121, 1794

Offset

1,7

Comments

Row sums are:{0, 1, 2, 4, 17, 52, 176, 537, 1550, 4323}.

Links

Table of n, a(n) for n=1..55.

Formula

a(n)=A000045(n)+1;b(n)=A000045(n+1)-1; t(n,m)=a(m)*(a(n) + 1) - If[ m < n, Round[(a(m) - 1)/a(n) + 1], a(n) + 1]*a(n).

Example

{0},
{0, 1},
{0, 1, 1},
{-3, 1, 1, 5},
{-5, 1, 1, 7, 13},
{-8, 1, 1, 10, 19, 29},
{-13, 1, 1, 15, 29, 57, 86},
{-21,1, 1, 23, 45, 89, 155, 244},
{-34, 1, 1, 36, 71, 141, 246, 421, 667},
{-55, 1, 1, 57, 113, 225, 393, 673, 1121, 1794}

Mathematica

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

Crossrefs

Cf. A000045.

Sequence in context: A238339 A302997 A326792 * A106597 A108359 A100936

Adjacent sequences: A144458 A144459 A144460 * A144462 A144463 A144464

Keyword

uned,sign

Author

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

Status

approved