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A209699 Triangle of coefficients of polynomials u(n,x) jointly generated with A209700; see the Formula section. 3
1, 0, 2, 0, 2, 4, 0, 3, 4, 8, 0, 4, 5, 12, 16, 0, 5, 6, 19, 28, 32, 0, 6, 7, 28, 45, 68, 64, 0, 7, 8, 39, 66, 123, 156, 128, 0, 8, 9, 52, 91, 200, 301, 356, 256, 0, 9, 10, 67, 120, 303, 510, 747, 796, 512, 0, 10, 11, 84, 153, 436, 795, 1356, 1789, 1764, 1024, 0, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
For a discussion and guide to related arrays, see A208510.
LINKS
FORMULA
u(n,x)=x*u(n-1,x)+x*v(n-1,x),
v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
0...2
0...2...4
0...3...4...8
0...4...5...12...16
First three polynomials v(n,x): 1, 2x, 2x + 4x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := 2 x*u[n - 1, 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[%] (* A209699 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209700 *)
CROSSREFS
Sequence in context: A199335 A141660 A368500 * A115273 A194759 A209697
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 12 2012
STATUS
approved

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Last modified June 18 10:36 EDT 2024. Contains 373479 sequences. (Running on oeis4.)