|
|
A193970
|
|
Mirror of the triangle A193969.
|
|
2
|
|
|
1, 3, 1, 7, 4, 1, 21, 12, 7, 2, 54, 33, 19, 11, 3, 144, 88, 54, 31, 18, 5, 376, 232, 142, 87, 50, 29, 8, 987, 609, 376, 230, 141, 81, 47, 13, 2583, 1596, 985, 608, 372, 228, 131, 76, 21, 6765, 4180, 2583, 1594, 984, 602, 369, 212, 123, 34, 17710, 10945, 6763
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Write w(n,k) for the triangle at A193969. The triangle at A193970 is then given by w(n,n-k).
|
|
EXAMPLE
|
First six rows:
1
3....1
7....4....1
21...12...7....2
54...33...19...11...3
144..88...54...31...18...5
|
|
MATHEMATICA
|
z = 12;
p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
q[n_, x_] := Sum[LucasL[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}]] (* A193969 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193970 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|