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A210228
Triangle of coefficients of polynomials v(n,x) jointly generated with A210227; see the Formula section.
3
1, 1, 4, 1, 6, 10, 1, 6, 24, 22, 1, 6, 28, 80, 46, 1, 6, 28, 120, 236, 94, 1, 6, 28, 128, 464, 640, 190, 1, 6, 28, 128, 568, 1624, 1636, 382, 1, 6, 28, 128, 584, 2376, 5224, 4008, 766, 1, 6, 28, 128, 584, 2632, 9240, 15696, 9516, 1534, 1, 6, 28, 128, 584
OFFSET
1,3
COMMENTS
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
v(n,x)=2x*u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...4
1...6...10
1...6...24...22
1...6...28...80...46
First three polynomials v(n,x): 1, 1 + 4x , 1 + 6x + 19x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := 2 x*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]
Flatten[%] (* A210227 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210228 *)
CROSSREFS
Sequence in context: A154905 A124739 A122662 * A209161 A338171 A333824
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 20 2012
STATUS
approved