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

Author

Clark Kimberling, Jul 31 2011

Keywords

• nonn
• tabl

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.

Examples

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

Crossrefs

Cf. A193091, A058071, A003266, A191994.

Programs

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}]]