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A193924 Mirror of the triangle A193923. 2
1, 1, 1, 3, 2, 1, 8, 5, 3, 1, 21, 13, 8, 4, 1, 55, 34, 21, 12, 5, 1, 144, 89, 55, 33, 17, 6, 1, 377, 233, 144, 88, 50, 23, 7, 1, 987, 610, 377, 232, 138, 73, 30, 8, 1, 2584, 1597, 987, 609, 370, 211, 103, 38, 9, 1, 6765, 4181, 2584, 1596, 979, 581, 314, 141, 47 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A193924 is obtained by reversing the rows of the triangle A193923.

LINKS

Table of n, a(n) for n=0..63.

FORMULA

Write w(n,k) for the triangle at A193923.  The triangle at A193924 is then given by w(n,n-k).

EXAMPLE

First six rows:

1

1....1

3....2....1

8....5....3....1

21...13...8....4....1

55...34...21...12...5...1

MATHEMATICA

p[n_, x_] := (x + 1)^n;

q[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];

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}]]  (* A193923 *)

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

Flatten[Table[g[n], {n, -1, z}]]  (* A193924 *)

CROSSREFS

Cf. A193923.

Sequence in context: A158474 A090452 A305538 * A110439 A327917 A065602

Adjacent sequences:  A193921 A193922 A193923 * A193925 A193926 A193927

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 09 2011

STATUS

approved

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Last modified January 22 22:16 EST 2020. Contains 331166 sequences. (Running on oeis4.)