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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
OFFSET
0,4
COMMENTS
A193924 is obtained by reversing the rows of the triangle A193923.
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: A090452 A305538 A370527 * A110439 A327917 A065602
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 09 2011
STATUS
approved