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A210601
Triangle of coefficients of polynomials v(n,x) jointly generated with A210600; see the Formula section.
3
1, 3, 2, 6, 9, 4, 11, 26, 24, 8, 19, 63, 89, 60, 16, 32, 138, 265, 270, 144, 32, 53, 284, 693, 949, 760, 336, 64, 87, 560, 1664, 2870, 3072, 2032, 768, 128, 142, 1071, 3761, 7840, 10521, 9272, 5232, 1728, 256, 231, 2002, 8127, 19896, 32143, 35418
OFFSET
1,2
COMMENTS
Row n starts with n and ends with an even-indexed Fibonacci number. For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
v(n,x)=(x+1)*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
3....2
6....9....4
11...26...24...8
19...63...89...60...16
First three polynomials v(n,x): 1, 3 + 2x, 6 + 9x + 4x^2
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*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[%] (* A210600 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210601 *)
CROSSREFS
Sequence in context: A352877 A210754 A210738 * A197493 A300070 A171632
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 24 2012
STATUS
approved