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A193667 Triangular array:  the fission of (p(n,x)) by (q(n,x)), where p(n,x)=(x+1^n and q(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers). 2
1, 1, 3, 1, 4, 8, 1, 5, 12, 21, 1, 6, 17, 33, 55, 1, 7, 23, 50, 88, 144, 1, 8, 30, 73, 138, 232, 377, 1, 9, 38, 103, 211, 370, 609, 987, 1, 10, 47, 141, 314, 581, 979, 1596, 2584, 1, 11, 57, 188, 455, 895, 1560, 2575, 4180, 6765, 1, 12, 68, 245, 643, 1350, 2455 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

See A193842 for the definition of the fission of P by Q, where P and Q are sequences of polynomials or triangular arrays (of coefficients of polynomials).  A193667 is the mirror of A125172.

LINKS

Table of n, a(n) for n=0..61.

EXAMPLE

First six rows:

1

1...3

1...4...8

1...5...12...21

1...6...17...33...55

1...7...23...50...88...144

MATHEMATICA

z = 11;

p[n_, x_] := (x + 1)^n;

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

p1[n_, k_] := Coefficient[p[n, x], x^k];

p1[n_, 0] := p[n, x] /. x -> 0;

d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]

h[n_] := CoefficientList[d[n, x], {x}]

TableForm[Table[Reverse[h[n]], {n, 0, z}]]

Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193667 *)

TableForm[Table[h[n], {n, 0, z}]]

Flatten[Table[h[n], {n, -1, z}]]  (* A125172 *)

CROSSREFS

Cf. A193842, A125172.

Sequence in context: A005371 A210739 A193605 * A205878 A329130 A057049

Adjacent sequences:  A193664 A193665 A193666 * A193668 A193669 A193670

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 11 2011

STATUS

approved

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Last modified August 5 00:15 EDT 2021. Contains 346456 sequences. (Running on oeis4.)