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A193920 Mirror of the triangle A193919. 2
1, 1, 1, 2, 3, 1, 4, 9, 7, 2, 7, 21, 25, 14, 3, 12, 46, 75, 64, 28, 5, 20, 94, 195, 224, 148, 53, 8, 33, 185, 468, 679, 603, 326, 99, 13, 54, 353, 1056, 1855, 2073, 1502, 687, 181, 21, 88, 659, 2280, 4711, 6357, 5786, 3543, 1405, 327, 34, 143, 1209, 4755 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
A193920 is obtained by reversing the rows of the triangle A193919.
LINKS
FORMULA
Write w(n,k) for the triangle at A193919. The triangle at A193920 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
1....1
2....3....1
4....9....7....2
7....21...25...14...3
12...46...75...64...28...5
MATHEMATICA
p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
q[n_, x_] := (x + 1)^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}]] (* A193919 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193920 *)
CROSSREFS
Cf. A193919.
Sequence in context: A165241 A119865 A177896 * A076732 A130152 A211233
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 09 2011
STATUS
approved

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Last modified April 22 02:54 EDT 2024. Contains 371887 sequences. (Running on oeis4.)