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A193903
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Mirror of the triangle A193902.
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2
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1, 1, 2, 3, 6, 4, 7, 14, 12, 8, 15, 30, 28, 24, 16, 31, 62, 60, 56, 48, 32, 63, 126, 124, 120, 112, 96, 64, 127, 254, 252, 248, 240, 224, 192, 128, 255, 510, 508, 504, 496, 480, 448, 384, 256, 511, 1022, 1020, 1016, 1008, 992, 960, 896, 768, 512, 1023, 2046
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OFFSET
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0,3
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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 A193902. The triangle at A193903 is then given by w(n,n-k).
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EXAMPLE
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First six rows:
1
1....2
3....6....4
7....14...12...8
15...30...28...24...16
31...62...60...56...48...32
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MATHEMATICA
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z = 12;
p[n_, x_] := x*p[n - 1, x] + 2^n; p[0, x_] := 1;
q[n_, x_] := 2 x*q[n - 1, x] + 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}]] (* A193902 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193903 *)
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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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