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A193958
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Mirror of the triangle A193955.
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2
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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
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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Write w(n,k) for the triangle at A193957. The triangle at A193958 is then given by w(n,n-k).
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EXAMPLE
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First six rows:
1
1....1
5....3....1
14...9....5...3
34...21...13..7...4
74...46...28..17..9..5
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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