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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) . 2
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 (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..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

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Last modified May 21 05:37 EDT 2022. Contains 353889 sequences. (Running on oeis4.)