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A193595 Augmentation of the Fibonacci triangle A058071.  See Comments. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified April 20 05:31 EDT 2021. Contains 343121 sequences. (Running on oeis4.)