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A210749
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Triangle of coefficients of polynomials u(n,x) jointly generated with A210750; see the Formula section.
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3
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1, 3, 1, 6, 7, 1, 11, 21, 15, 1, 19, 53, 60, 31, 1, 32, 118, 191, 155, 63, 1, 53, 246, 514, 593, 378, 127, 1, 87, 489, 1261, 1863, 1683, 889, 255, 1, 142, 941, 2890, 5233, 6029, 4501, 2040, 511, 1, 231, 1767, 6311, 13527, 19026, 18068, 11543, 4599
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OFFSET
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1,2
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COMMENTS
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Row n starts with -2+F(n+3) and ends with 1, where F=A000045 (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+1)*u(n-1,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
3....1
6....7....1
11...21...15...1
19...53...60...31...1
First three polynomials u(n,x): 1, 3+ x, 6 + 7x + 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 + 1)*u[n - 1, 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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