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A209694
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Triangle of coefficients of polynomials v(n,x) jointly generated with A209693; see the Formula section.
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3
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1, 3, 1, 4, 6, 1, 5, 13, 10, 1, 6, 22, 32, 15, 1, 7, 33, 71, 66, 21, 1, 8, 46, 131, 186, 121, 28, 1, 9, 61, 216, 415, 422, 204, 36, 1, 10, 78, 330, 801, 1121, 862, 323, 45, 1, 11, 97, 477, 1400, 2507, 2689, 1625, 487, 55, 1, 12, 118, 661, 2276, 4977, 6902
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OFFSET
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1,2
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COMMENTS
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Alternating row sums are periodic. 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)+x*v(n-1,x),
v(n,x)=u(n-1,x)+(x+1)*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
3...1
4...6....1
5...13...10...1
6...22...32...15...1
First three polynomials v(n,x): 1, 3 + x , 4 + 6x + x^2.
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MATHEMATICA
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u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := u[n - 1, x] + (x + 1)*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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