A193595 Augmentation of the Fibonacci triangle A058071. See Comments.

1, 1, 1, 2, 2, 3, 6, 8, 9, 13, 30, 42, 58, 56, 85, 240, 360, 480, 576, 533, 821, 3120, 4800, 6600, 7488, 8698, 7666, 12015, 65520, 102960, 141120, 165240, 178158, 200200, 171501, 271601, 2227680, 3538080, 4876560, 5670720, 6310590, 6513474

Offset

0,4

Comments

For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.

Regarding A193595, (column 1)=A003266, (column 2)=A191994.

Links

Table of n, a(n) for n=0..41.

Example

First 5 rows of A193589:
1
1....1
2....2....3
6....8....9....13
30...42...58...56...85

Mathematica

p[n_, k_] := Fibonacci[k + 1]*Fibonacci[n + 1 - k]
Table[p[n, k], {n, 0, 5}, {k, 0,
  n}]  (* A058071, a Fibonacci triangle *)
m[n_] := Table[If[i <= j, p[n + 1 - i, j - i], 0], {i, n}, {j, n + 1}]
TableForm[m[4]]
w[0, 0] = 1; w[1, 0] = p[1, 0]; w[1, 1] = p[1, 1];
v[0] = w[0, 0]; v[1] = {w[1, 0], w[1, 1]};
v[n_] := v[n - 1].m[n]
TableForm[Table[v[n], {n, 0, 10}]]  (* A193595 *)
Flatten[Table[v[n], {n, 0, 9}]]

Crossrefs

Cf. A193091, A058071, A003266, A191994.

Sequence in context: A159915 A007801 A275493 * A077871 A215450 A300352

Adjacent sequences: A193592 A193593 A193594 * A193596 A193597 A193598

Keyword

nonn,tabl

Author

Clark Kimberling, Jul 31 2011

Status

approved