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A210564
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Triangle of coefficients of polynomials v(n,x) jointly generated with A210563; see the Formula section.
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3
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1, 2, 3, 2, 7, 8, 2, 8, 22, 21, 2, 8, 29, 67, 55, 2, 8, 30, 101, 200, 144, 2, 8, 30, 111, 341, 588, 377, 2, 8, 30, 112, 404, 1122, 1708, 987, 2, 8, 30, 112, 417, 1442, 3613, 4913, 2584, 2, 8, 30, 112, 418, 1543, 5044, 11425, 14018, 6765, 2, 8, 30, 112, 418
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OFFSET
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1,2
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COMMENTS
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Last terms in rows: even-indexed 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)+x*v(n-1,x)+1,
v(n,x)=(x+1)*u(n-1,x)+2x*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...3
2...7...8
2...8...22...21
2...8...29...67...55
First three polynomials v(n,x): 1, 2 + 3x , 2 + 8x + 22x^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] + 1;
v[n_, x_] := (x + 1)*u[n - 1, x] + 2 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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