A193951 Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{(k+1)(n+1)*x^(n-k) : 0<=k<=n} and q(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers).

1, 1, 1, 4, 6, 10, 9, 15, 27, 42, 16, 28, 52, 84, 136, 25, 45, 85, 140, 230, 370, 36, 66, 126, 210, 348, 564, 912, 49, 91, 175, 294, 490, 798, 1295, 2093, 64, 120, 232, 392, 656, 1072, 1744, 2824, 4568, 81, 153, 297, 504, 846, 1386, 2259, 3663, 5931, 9594

Offset

0,4

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..54.

Example

First six rows:
1
1....1
4....6....10
9....15...27...42
16...28...52...84....136
25...45...85...140...230...370

Mathematica

z = 12;
p[n_, x_] := Sum[(k + 1) (n + 1)*x^(n - k), {k, 0, n}];
q[n_, x_] := Sum[Fibonacci[k + 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}]]  (* A193951 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193952 *)

Crossrefs

Cf. A193722, A193952, A193949.

Sequence in context: A117622 A188673 A365448 * A129854 A088682 A102415

Adjacent sequences: A193948 A193949 A193950 * A193952 A193953 A193954

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved