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A193968
Mirror of the triangle A193967.
2
1, 1, 1, 7, 4, 3, 19, 12, 7, 4, 54, 33, 21, 11, 7, 142, 88, 54, 33, 18, 11, 376, 232, 144, 87, 54, 29, 18, 985, 609, 376, 232, 141, 87, 47, 29, 2583, 1596, 987, 608, 376, 228, 141, 76, 47, 6763, 4180, 2583, 1596, 984, 608, 369, 228, 123, 76, 17710, 10945
OFFSET
0,4
COMMENTS
A193967 is obtained by reversing the rows of the triangle A193968.
FORMULA
Write w(n,k) for the triangle at A193967. The triangle at A193968 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
1....1
7....4....3
19...12...7...4
54...33...21..11..7
142..88...54..33..18..11
MATHEMATICA
z = 12;
p[n_, x_] := Sum[LucasL[k + 1]*x^(n - k), {k, 0, 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}]] (* A193967 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193968 *)
CROSSREFS
Cf. A193968.
Sequence in context: A065477 A272526 A100041 * A153840 A198351 A354249
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 10 2011
STATUS
approved