A193903 Mirror of the triangle A193902.

1, 1, 2, 3, 6, 4, 7, 14, 12, 8, 15, 30, 28, 24, 16, 31, 62, 60, 56, 48, 32, 63, 126, 124, 120, 112, 96, 64, 127, 254, 252, 248, 240, 224, 192, 128, 255, 510, 508, 504, 496, 480, 448, 384, 256, 511, 1022, 1020, 1016, 1008, 992, 960, 896, 768, 512, 1023, 2046

Offset

0,3

Comments

A193903 is obtained by reversing the rows of the triangle A193902.

Links

Table of n, a(n) for n=0..56.

Formula

Write w(n,k) for the triangle at A193902. The triangle at A193903 is then given by w(n,n-k).

Example

First six rows:
1
1....2
3....6....4
7....14...12...8
15...30...28...24...16
31...62...60...56...48...32

Mathematica

z = 12;
p[n_, x_] := x*p[n - 1, x] + 2^n; p[0, x_] := 1;
q[n_, x_] := 2 x*q[n - 1, x] + 1; q[0, x_] := 1;
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}]]  (* A193902 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193903 *)

Crossrefs

Cf. A193902.

Sequence in context: A266191 A273338 A099900 * A138728 A291604 A082332

Adjacent sequences: A193900 A193901 A193902 * A193904 A193905 A193906

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 08 2011

Status

approved