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A210598
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Triangle of coefficients of polynomials u(n,x) jointly generated with A210599; see the Formula section.
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3
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1, 2, 2, 3, 7, 5, 4, 14, 23, 13, 5, 24, 58, 72, 34, 6, 36, 119, 219, 219, 89, 7, 51, 209, 521, 777, 653, 233, 8, 68, 338, 1048, 2101, 2639, 1918, 610, 9, 88, 508, 1902, 4754, 7989, 8679, 5567, 1597, 10, 110, 730, 3180, 9565, 20055, 29062, 27844, 16003
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OFFSET
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1,2
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COMMENTS
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Row n starts with n and ends with an odd-indexed
Fibonacci number. For a discussion and guide to related
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LINKS
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FORMULA
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u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
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...2
3...7....5
4...14...23...13
5...24...58...72...34
First three polynomials u(n,x): 1, 2+ 2x, 3 + 7x + 5x^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 + 1)*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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