A193822 Mirror of the triangle A193821.

1, 1, 1, 3, 3, 2, 9, 9, 8, 4, 27, 27, 26, 20, 8, 81, 81, 80, 72, 48, 16, 243, 243, 242, 232, 192, 112, 32, 729, 729, 728, 716, 656, 496, 256, 64, 2187, 2187, 2186, 2172, 2088, 1808, 1248, 576, 128, 6561, 6561, 6560, 6544, 6432, 5984, 4864, 3072, 1280, 256

Offset

0,4

Comments

A193822 is obtained by reversing the rows of the triangle A193821.

Links

Table of n, a(n) for n=0..54.

Formula

Write w(n,k) for the triangle at A193821. The triangle at A193822 is then given by w(n,n-k).

Example

First six rows:
1
1....1
3....3....2
9....9....8.....4
27...27...26....20...8
81...81...80....72...48...16

Mathematica

p[n_, x_] := (a*x + b)^n
q[0, x_] := 1
q[n_, x_] := x*q[n - 1, x] + 1; q[n_, 0] := q[n, x] /. x -> 0;
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}]]   (* A193821 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193822 *)

Crossrefs

Cf. A193722, A193821.

Sequence in context: A286952 A100052 A128504 * A202699 A058137 A250304

Adjacent sequences: A193819 A193820 A193821 * A193823 A193824 A193825

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 06 2011

Status

approved