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A193957 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}. 2
1, 1, 1, 2, 3, 5, 3, 5, 9, 14, 4, 7, 13, 21, 34, 5, 9, 17, 28, 46, 74, 6, 11, 21, 35, 58, 94, 152, 7, 13, 25, 42, 70, 114, 185, 299, 8, 15, 29, 49, 82, 134, 218, 353, 571, 9, 17, 33, 56, 94, 154, 251, 407, 659, 1066, 10, 19, 37, 63, 106, 174, 284, 461, 747, 1209 (list; table; graph; refs; listen; history; text; internal format)
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..64.

EXAMPLE

First six rows:

1

1...1

2...3...5

3...5...9....14

4...7...13...21...34

5...9...17...28...46...74

MATHEMATICA

z = 12;

p[n_, x_] := x*p[n - 1, x] + n + 1; p[0, x_] := 1 ;

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}]]  (* A193957 *)

TableForm[Table[g[n], {n, -1, z}]]

Flatten[Table[g[n], {n, -1, z}]]  (* A193958 *)

CROSSREFS

Cf. A193722, A193958.

Sequence in context: A261324 A224887 A151571 * A336746 A209769 A114230

Adjacent sequences:  A193954 A193955 A193956 * A193958 A193959 A193960

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved

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Last modified May 26 11:30 EDT 2022. Contains 354086 sequences. (Running on oeis4.)