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A209166
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Triangle of coefficients of polynomials u(n,x) jointly generated with A209167; see the Formula section.
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3
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1, 2, 1, 4, 5, 2, 7, 13, 10, 3, 12, 30, 34, 20, 5, 20, 63, 94, 80, 38, 8, 33, 126, 233, 258, 177, 71, 13, 54, 243, 536, 728, 647, 374, 130, 21, 88, 457, 1171, 1881, 2043, 1527, 765, 235, 34, 143, 843, 2461, 4559, 5835, 5319, 3443, 1525, 420, 55, 232
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OFFSET
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1,2
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COMMENTS
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Row n begins with F(n+2)-1 and ends with F(n), where F=A000045 (Fibonacci numbers).
Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
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)=u(n-1,x)+(x+1)*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 five rows:
1
2....1
5....5....1
11...15...6....1
23...41...27...9...1
First three polynomials v(n,x): 1, 2 + x, 5 + 5x + x^2.
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MATHEMATICA
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u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + 1)*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]
Table[Expand[v[n, x]], {n, 1, z}]
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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