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| NAME
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allocatedTriangle of coefficients of polynomials u(n,x) jointly generated with A210034; see forthe ClarkFormula Kimberlingsection.
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| DATA
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1, 3, 6, 1, 11, 3, 1, 19, 8, 3, 1, 32, 18, 9, 3, 1, 53, 38, 22, 10, 3, 1, 87, 76, 51, 26, 11, 3, 1, 142, 147, 111, 65, 30, 12, 3, 1, 231, 277, 233, 151, 80, 34, 13, 3, 1, 375, 512, 474, 338, 196, 96, 38, 14, 3, 1, 608, 932, 942, 730, 463, 246, 113, 42, 15, 3, 1
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| OFFSET
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1,2
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| COMMENTS
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For a discussion and guide to related arrays, see A208510.
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| FORMULA
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u(n,x)=u(n-1,x)+v(n-1,x)+1,
v(n,x)=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
3
6....1
11...3...1
19...8...3...1
First three polynomials u(n,x): 1, 3, 6 + x.
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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] + v[n - 1, x] + 1;
v[n_, x_] := 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]
Flatten[%] (* A210033 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210034 *)
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| CROSSREFS
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Cf. A210034, A208510.
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| KEYWORD
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allocated
nonn,tabf
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| AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Mar 16 2012
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| STATUS
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approved
editing
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