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A193903 Mirror of the triangle A193902. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified February 16 21:31 EST 2020. Contains 331975 sequences. (Running on oeis4.)