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A193954
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Mirror of the triangle A193953.
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2
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1, 2, 1, 5, 3, 1, 13, 9, 5, 2, 28, 21, 14, 8, 3, 58, 46, 34, 23, 13, 5, 114, 94, 74, 55, 37, 21, 8, 218, 185, 152, 120, 89, 60, 34, 13, 407, 353, 299, 246, 194, 144, 97, 55, 21, 747, 659, 571, 484, 398, 314, 233, 157, 89, 34, 1352, 1209, 1066, 924, 783, 644
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OFFSET
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0,2
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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 A193953. The triangle at A193954 is then given by w(n,n-k).
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EXAMPLE
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First six rows:
1
2....1
5....3....1
13...9....5....2
28...21...14...8...3
58...46...34...23..13..5
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MATHEMATICA
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z = 12;
p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
q[n_, x_] := x*q[n - 1, x] + n + 1; q[0, x_] := 1
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}]] (* A193953 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193954 *)
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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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