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A193958
Mirror of the triangle A193955.
2
1, 1, 1, 5, 3, 2, 14, 9, 5, 3, 34, 21, 13, 7, 4, 74, 46, 28, 17, 9, 5, 152, 94, 58, 35, 21, 11, 6, 299, 185, 114, 70, 42, 25, 13, 7, 571, 353, 218, 134, 82, 49, 29, 15, 8, 1066, 659, 407, 251, 154, 94, 56, 33, 17, 9, 1956, 1209, 747, 461, 284, 174, 106, 63, 37
OFFSET
0,4
COMMENTS
A193958 is obtained by reversing the rows of the triangle A193957.
FORMULA
Write w(n,k) for the triangle at A193957. The triangle at A193958 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
1....1
5....3....1
14...9....5...3
34...21...13..7...4
74...46...28..17..9..5
MATHEMATICA
z = 12;
p[n_, x_] := x*p[n - 1, x] + n + 1; p[0, x_] := 1 ;
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}]] (* A193957 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193958 *)
CROSSREFS
Cf. A193957.
Sequence in context: A309276 A268690 A065627 * A322289 A259228 A241182
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 10 2011
STATUS
approved