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A193850 Triangular array:  the fission of ((x+2)^n) by (q(n,x)) given by q(n,x)=x^n+x^(n-1)+...+x+1. 4
2, 4, 8, 8, 20, 26, 16, 48, 72, 80, 32, 112, 192, 232, 242, 64, 256, 496, 656, 716, 728, 128, 576, 1248, 1808, 2088, 2172, 2186, 256, 1280, 3072, 4864, 5984, 6432, 6544, 6560, 512, 2816, 7424, 12800, 16832, 18848, 19520, 19664, 19682, 1024, 6144 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

See A193842 for the definition of fission of two sequences of polynomials or triangular arrays.

LINKS

Table of n, a(n) for n=0..46.

EXAMPLE

First six rows:

2

4....8

8....20....26

16...48....72....80

32...112...192...232....242

64...256...496...656....716...728

MATHEMATICA

z = 10;

p[n_, x_] := (x + 2)^n;

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

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}]]  (* A193850 *)

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

Flatten[Table[h[n], {n, -1, z}]]   (* A193851  *)

TableForm[Table[Reverse[h[n]/2], {n, 0, z}]]

Flatten[Table[Reverse[h[n]]/2, {n, -1, z}]] (* A193852 *)

TableForm[Table[h[n]/2, {n, 0, z}]]

Flatten[Table[h[n]/2, {n, -1, z}]]  (* A193853 *)

CROSSREFS

Cf. A193842, A193850, A193852.

Sequence in context: A132720 A029930 A334284 * A140119 A273068 A193846

Adjacent sequences:  A193847 A193848 A193849 * A193851 A193852 A193853

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 07 2011

STATUS

approved

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Last modified October 19 07:50 EDT 2021. Contains 348074 sequences. (Running on oeis4.)