login
A193909
Mirror of the triangle A193908.
3
1, 1, 2, 3, 6, 8, 6, 12, 20, 24, 11, 22, 40, 64, 80, 19, 38, 72, 128, 208, 256, 32, 64, 124, 232, 416, 672, 832, 53, 106, 208, 400, 752, 1344, 2176, 2688, 87, 174, 344, 672, 1296, 2432, 4352, 7040, 8704, 142, 284, 564, 1112, 2176, 4192, 7872, 14080, 22784
OFFSET
0,3
COMMENTS
A193909 is obtained by reversing the rows of the triangle A193908.
FORMULA
Write w(n,k) for the triangle at A193908. The triangle at A193909 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
1....2
3....6....8
6....12...20...24
11...22...40...64....80
19...38...72...128...208...256
MATHEMATICA
z = 12;
p[n_, x_] := Sum[Fibonacci[k + 2]*x^(n - k), {k, 0, n}];
q[n_, x_] := 2 x*q[n - 1, x] + 1 ; q[0, x_] := 1;
t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;
w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
g[n_] := CoefficientList[w[n, x], {x}]
TableForm[Table[Reverse[g[n]], {n, -1, z}]]
Flatten[Table[Reverse[g[n]], {n, -1, z}]] (* A193908 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193909 *)
CROSSREFS
Cf. A193908.
Sequence in context: A246266 A284385 A282940 * A211603 A221956 A249549
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 09 2011
STATUS
approved