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A210879
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Triangle of coefficients of polynomials v(n,x) jointly generated with A210878; see the Formula section.
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3
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1, 2, 2, 1, 5, 5, 1, 5, 16, 12, 1, 3, 21, 47, 29, 1, 3, 17, 79, 134, 70, 1, 3, 13, 79, 273, 373, 169, 1, 3, 13, 63, 333, 893, 1020, 408, 1, 3, 13, 55, 297, 1291, 2805, 2751, 985, 1, 3, 13, 55, 249, 1323, 4701, 8543, 7338, 2378, 1, 3, 13, 55, 233, 1147, 5525
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OFFSET
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1,2
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COMMENTS
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Leading coefficient of v(n,x): A000129
Alternating row sums: 1,0,1,0,1,0,1,0,1,0,...
Limiting row: 1,3,13,55,233,987...( Fibonacci numbers)
For a discussion and guide to related arrays, see A208510.
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LINKS
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FORMULA
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u(n,x)=x*u(n-1,x)+2x*v(n-1,x),
v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
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EXAMPLE
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First six rows:
1
2...2
1...5...5
1...5...16...12
1...3...21...47....29
1...3...17...79...134...70
First three polynomials v(n,x): 1, 2 + 2x, 1 + 5x + 5x^2
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MATHEMATICA
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u[1, x_] := 1; v[1, x_] := 1; z = 14;
u[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x];
v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
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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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