OFFSET
0,2
COMMENTS
See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.
First five rows of P (triangle of coefficients of polynomials p(n,x)):
1
1...2
1...2...3
1...2...3...5
1...2...3...5...8
First five rows of Q:
1
2...1
4...2..1
8...4...2...1
16..8...4...2...1
EXAMPLE
First six rows:
1
2....1
8....6....3
24...20...12...6
80...64...40...22...11
256..208..128..72...38...19
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
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 09 2011
STATUS
approved