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A193960
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Mirror of the triangle A193959.
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2
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1, 1, 1, 9, 5, 4, 36, 23, 13, 9, 116, 71, 45, 25, 16, 316, 196, 120, 75, 41, 25, 784, 484, 300, 183, 113, 61, 36, 1813, 1121, 692, 428, 260, 159, 85, 49, 3989, 2465, 1524, 940, 580, 351, 213, 113, 64, 8444, 5219, 3225, 1993, 1228, 756, 456, 275, 145, 81
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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 A193959. The triangle at A193960 is then given by w(n,n-k).
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EXAMPLE
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First six rows:
1
1.....1
9.....5....4
36....23...13...9
116...71...45...25..16
316...196..120..75..41..25
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MATHEMATICA
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z = 12;
p[n_, x_] := Sum[((k + 1)^2)*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}]] (* A193959 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193960 *)
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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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