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A193949 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}. 3
1, 2, 4, 3, 8, 13, 8, 19, 32, 45, 15, 38, 64, 92, 120, 30, 75, 128, 184, 242, 300, 56, 142, 243, 352, 464, 578, 692, 104, 264, 454, 659, 872, 1088, 1306, 1524, 189, 482, 831, 1210, 1604, 2006, 2411, 2818, 3225, 340, 869, 1502, 2191, 2910, 3644, 4386 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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..51.

EXAMPLE

First six rows:

1

2....4

3....8....13

8....19...32...45

15...38...64...92...120

30...75...128..184..242..300

MATHEMATICA

z = 12;

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

q[n_, x_] := Sum[(k + 1) (n + 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}]]  (* A193949 *)

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

Flatten[Table[g[n], {n, -1, z}]]  (* A193950 *)

CROSSREFS

Cf. A193722, A193950.

Sequence in context: A253722 A323506 A302747 * A246679 A244153 A308328

Adjacent sequences:  A193946 A193947 A193948 * A193950 A193951 A193952

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved

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Last modified April 23 10:51 EDT 2021. Contains 343204 sequences. (Running on oeis4.)