A193847 Mirror of the triangle A193846.

2, 8, 4, 26, 28, 8, 80, 136, 80, 16, 242, 568, 512, 208, 32, 728, 2188, 2672, 1648, 512, 64, 2186, 8020, 12392, 10288, 4832, 1216, 128, 6560, 28432, 53216, 55648, 35072, 13312, 2816, 256, 19682, 98416, 216512, 273376, 216512, 110080, 35072

Offset: 0

Author

Clark Kimberling, Aug 07 2011

Keywords

• nonn
• tabl

Comments

A193847 is obtained by reversing the rows of the triangle A193846.

Examples

			First six rows:
2
8.....4
26....28....8
80....136...80....16
242...568...512...208...32
728...2188..2672..1648..512..64
		

Crossrefs

Cf. A193846, A193849.

Programs

Mathematica

p[n_, x_] := (x + 2)^n;
q[n_, x_] := (x + 1)^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}]]   (* A193846 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]]  (* A193847 *)
TableForm[Table[Reverse[h[n]/2], {n, 0, z}]]
Flatten[Table[Reverse[h[n]]/2, {n, -1, z}]] (* A193848 *)
TableForm[Table[h[n]/2, {n, 0, z}]]
Flatten[Table[h[n]/2, {n, -1, z}]]  (* A193849 *)

Formula

Write w(n,k) for the triangle at A193846. The triangle at A193847 is then given by w(n,n-k).