Revision History for A209819
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#6 by Russ Cox at Fri Mar 30 18:58:16 EDT 2012
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| AUTHOR
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_Clark Kimberling (ck6(AT)evansville.edu), _, Mar 23 2012
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Discussion
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| Fri Mar 30
| 18:58
| OEIS Server: https://oeis.org/edit/global/285
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#5 by T. D. Noe at Sat Mar 24 12:28:11 EDT 2012
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#4 by Clark Kimberling at Fri Mar 23 21:27:09 EDT 2012
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#3 by Clark Kimberling at Fri Mar 23 20:39:46 EDT 2012
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| COMMENTS
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Alternating row sums: 1,-2,3,-4,5,-6,7,-8,...
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#2 by Clark Kimberling at Fri Mar 23 20:35:00 EDT 2012
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| NAME
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allocatedTriangle of coefficients of polynomials u(n,x) jointly generated with A209820; see forthe ClarkFormula Kimberlingsection.
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| DATA
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1, 1, 3, 1, 5, 7, 1, 5, 17, 17, 1, 5, 21, 53, 41, 1, 5, 21, 81, 157, 99, 1, 5, 21, 89, 289, 449, 239, 1, 5, 21, 89, 361, 973, 1253, 577, 1, 5, 21, 89, 377, 1389, 3133, 3433, 1393, 1, 5, 21, 89, 377, 1565, 5085, 9745, 9273, 3363, 1, 5, 21, 89, 377, 1597, 6285
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| OFFSET
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1,3
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| COMMENTS
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Let T(n,k) be the general term.
T(n,n): A001333
T(n,n-1): A088210
Row sums: A003561
Limiting row: F(2), F(5),F(8),...where F=A000045 (Fibonacci numbers)
For a discussion and guide to related arrays, see A208510.
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| FORMULA
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u(n,x)=x*u(n-1,x)+2x*v(n-1,x)+1,
v(n,x)=(x+1)*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
1...3
1...5...7
1...5...17...17
1...5...21...53...41
First three polynomials u(n,x): 1, 1 + 3x, 1 + 5x + 7x^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] + 2 x*v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*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[%] (* A209819 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209820 *)
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| CROSSREFS
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Cf. A209820, A208510.
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| KEYWORD
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allocated
nonn,tabl
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| AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Mar 23 2012
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| STATUS
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approved
editing
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#1 by Clark Kimberling at Tue Mar 13 16:16:21 EDT 2012
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| NAME
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allocated for Clark Kimberling
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| KEYWORD
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allocated
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| STATUS
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approved
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