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A209697 Triangle of coefficients of polynomials u(n,x) jointly generated with A209698; see the Formula section. 3
1, 0, 2, 0, 2, 4, 0, 3, 6, 8, 0, 4, 10, 16, 16, 0, 5, 15, 30, 40, 32, 0, 6, 21, 50, 84, 96, 64, 0, 7, 28, 77, 154, 224, 224, 128, 0, 8, 36, 112, 258, 448, 576, 512, 256, 0, 9, 45, 156, 405, 810, 1248, 1440, 1152, 512, 0, 10, 55, 210, 605, 1362, 2420, 3360, 3520 (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)=x*u(n-1,x)+(x+1)*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....6...8
0...4...10...16...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_] := x*u[n - 1, x] + (x + 1)*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[%] (* A209697 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209698 *)
CROSSREFS
Sequence in context: A209699 A115273 A194759 * A126440 A131186 A137312
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 12 2012
STATUS
approved

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Last modified May 23 07:28 EDT 2024. Contains 372760 sequences. (Running on oeis4.)