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A193921 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)=x^n+x^(n-1)+...+x+1. 2
1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 3, 5, 6, 7, 7, 5, 8, 10, 11, 12, 12, 8, 13, 16, 18, 19, 20, 20, 13, 21, 26, 29, 31, 32, 33, 33, 21, 34, 42, 47, 50, 52, 53, 54, 54, 34, 55, 68, 76, 81, 84, 86, 87, 88, 88, 55, 89, 110, 123, 131, 136, 139, 141, 142, 143, 143, 89, 144, 178 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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..68.

EXAMPLE

First six rows:

1

1...1

1...2...2

2...3...4....4

3...5...6....7....7

5...8...10...11...12...12

MATHEMATICA

p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];

q[n_, x_] := x*q[n - 1, x] + 1; q[0, n_] := 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}]]  (* A193921 *)

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

Flatten[Table[g[n], {n, -1, z}]]  (* A193922 *)

CROSSREFS

Cf. A193722, A193922.

Sequence in context: A300401 A051601 A296612 * A074829 A060243 A054225

Adjacent sequences:  A193918 A193919 A193920 * A193922 A193923 A193924

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 09 2011

STATUS

approved

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Last modified May 28 17:37 EDT 2020. Contains 334684 sequences. (Running on oeis4.)