|
| |
|
|
A193900
|
|
Mirror of the triangle A193899.
|
|
2
|
|
|
|
1, 2, 1, 10, 5, 2, 42, 21, 10, 4, 170, 85, 42, 20, 8, 682, 341, 170, 84, 40, 16, 2730, 1365, 682, 340, 168, 80, 32, 10922, 5461, 2730, 1364, 680, 336, 160, 64, 43690, 21845, 10922, 5460, 2728, 1360, 672, 320, 128, 174762, 87381, 43690, 21844, 10920
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
|
|
|
LINKS
|
|
|
|
FORMULA
|
Write w(n,k) for the triangle at A193899. The triangle at A193900 is then given by w(n,n-k).
|
|
|
EXAMPLE
|
First six rows:
1
2.....1
10....5....2
42....21...10...4
170...85...42...20..8
682...341..170..84..40..16
|
|
|
MATHEMATICA
|
z = 12;
p[n_, x_] := x*p[n - 1, x] + 2^n; p[0, x_] := 1;
q[n_, x_] := p[n, x];
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}]] (* A193899 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193900 *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
