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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
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.
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
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jul 31 2011
STATUS
approved