A193949 Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers), and q(n,x)=sum{(k+1)(n+1)*x^(n-k) : 0<=k<=n}.

1, 2, 4, 3, 8, 13, 8, 19, 32, 45, 15, 38, 64, 92, 120, 30, 75, 128, 184, 242, 300, 56, 142, 243, 352, 464, 578, 692, 104, 264, 454, 659, 872, 1088, 1306, 1524, 189, 482, 831, 1210, 1604, 2006, 2411, 2818, 3225, 340, 869, 1502, 2191, 2910, 3644, 4386

Offset

0,2

Comments

See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.

Links

Table of n, a(n) for n=0..51.

Example

First six rows:
1
2....4
3....8....13
8....19...32...45
15...38...64...92...120
30...75...128..184..242..300

Mathematica

z = 12;
p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
q[n_, x_] := Sum[(k + 1) (n + 1)*x^(n - k), {k, 0, n}];
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}]]  (* A193949 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193950 *)

Crossrefs

Cf. A193722, A193950.

Sequence in context: A323506 A357988 A302747 * A246679 A244153 A366347

Adjacent sequences: A193946 A193947 A193948 * A193950 A193951 A193952

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved