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A193969 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{L(k+1)*x^(n-k) : 0<=k<=n}, where F=A000032 (Lucas numbers). 2
1, 1, 3, 1, 4, 7, 2, 7, 12, 21, 3, 11, 19, 33, 54, 5, 18, 31, 54, 88, 144, 8, 29, 50, 87, 142, 232, 376, 13, 47, 81, 141, 230, 376, 609, 987, 21, 76, 131, 228, 372, 608, 985, 1596, 2583, 34, 123, 212, 369, 602, 984, 1594, 2583, 4180, 6765, 55, 199, 343, 597 (list; table; graph; refs; listen; history; text; internal format)
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..58.

EXAMPLE

First six rows:

1

1...3

1...4...7

2...7...12...21

3...11..19...33...54

5...18..31...54...88...144

MATHEMATICA

z = 12;

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

q[n_, x_] := Sum[LucasL[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}]]  (* A193969 *)

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

Flatten[Table[g[n], {n, -1, z}]]  (* A193970 *)

CROSSREFS

Cf. A193722, A193970.

Sequence in context: A185722 A287376 A209418 * A169838 A249271 A272439

Adjacent sequences:  A193966 A193967 A193968 * A193970 A193971 A193972

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved

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Last modified October 22 13:49 EDT 2021. Contains 348170 sequences. (Running on oeis4.)