A193959 Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{((k+1)^2)*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, 4, 5, 9, 9, 13, 23, 36, 16, 25, 45, 71, 116, 25, 41, 75, 120, 196, 316, 36, 61, 113, 183, 300, 484, 784, 49, 85, 159, 260, 428, 692, 1121, 1813, 64, 113, 213, 351, 580, 940, 1524, 2465, 3989, 81, 145, 275, 456, 756, 1228, 1993, 3225, 5219, 8444

Offset

0,3

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..53.

Example

First six rows:
1
1....1
4....5....9
9....13...23...36
16...25...45...71....116
25...41...75...120...196...316

Mathematica

z = 12;
p[n_, x_] := Sum[((k + 1)^2)*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}]]  (* A193959 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193960 *)

Crossrefs

Cf. A193722, A193960 .

Sequence in context: A218505 A128891 A172180 * A093667 A243591 A189012

Adjacent sequences: A193956 A193957 A193958 * A193960 A193961 A193962

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved