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A193966
Mirror of the triangle A193965.
2
1, 3, 1, 15, 10, 3, 43, 26, 15, 4, 120, 75, 43, 25, 7, 318, 196, 120, 69, 40, 11, 840, 520, 318, 195, 112, 65, 18, 2203, 1361, 840, 514, 315, 181, 105, 29, 5775, 3570, 2203, 1360, 832, 510, 293, 170, 47, 15123, 9346, 5775, 3564, 2200, 1346, 825, 474
OFFSET
0,2
COMMENTS
A193966 is obtained by reversing the rows of the triangle A193965.
FORMULA
Write w(n,k) for the triangle at A193965. The triangle at A193966 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
3.....1
15....10...3
43....26...15...4
120...75...43...25..7
318...196..120..69..40..11
MATHEMATICA
z = 12;
p[n_, x_] := Sum[LucasL[k + 1]*x^(n - k), {k, 0, n}];
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}]] (* A193965 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193966 *)
CROSSREFS
Cf. A193965.
Sequence in context: A181996 A144006 A014621 * A366120 A113378 A365162
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 10 2011
STATUS
approved