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.

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

Offset: 0

Author

Clark Kimberling, Aug 07 2011

Keywords

• nonn
• tabl

Comments

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

Examples

			First six rows:
2
4....8
8....20....26
16...48....72....80
32...112...192...232....242
64...256...496...656....716...728
		

Crossrefs

Cf. A193842, A193850, A193852.

Programs

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 *)