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A193916 Mirror of the triangle A193915. 2
1, 1, 2, 2, 4, 4, 4, 8, 12, 16, 7, 14, 24, 40, 48, 12, 24, 44, 80, 128, 160, 20, 40, 76, 144, 256, 416, 512, 33, 66, 128, 248, 464, 832, 1344, 1664, 54, 108, 212, 416, 800, 1504, 2688, 4352, 5376, 88, 176, 348, 688, 1344, 2592, 4864, 8704, 14080, 17408 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A193916 is obtained by reversing the rows of the triangle A193915.

LINKS

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

FORMULA

Write w(n,k) for the triangle at A193915.  The triangle at A193916 is then given by w(n,n-k).

EXAMPLE

First six rows:

1

1....2

2....4....4

4....8....12...16

7....14...24...40...48

12...24...44...80...128...160

MATHEMATICA

z = 12;

p[n_, x_] := Sum[Fibonacci[k + 2]*x^(n - k), {k, 0, n}];

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}]]  (* A193908 *)

TableForm[Table[g[n], {n, -1, z}]]

Flatten[Table[g[n], {n, -1, z}]]  (* A193909 *)

CROSSREFS

Cf. A193915, A193909.

Sequence in context: A306060 A317238 A260038 * A304347 A316218 A305642

Adjacent sequences:  A193913 A193914 A193915 * A193917 A193918 A193919

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 09 2011

STATUS

approved

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Last modified October 26 05:22 EDT 2021. Contains 348256 sequences. (Running on oeis4.)