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A209760
Triangle of coefficients of polynomials v(n,x) jointly generated with A209759; see the Formula section.
3
1, 1, 3, 1, 3, 8, 1, 3, 11, 21, 1, 3, 11, 38, 55, 1, 3, 11, 41, 124, 144, 1, 3, 11, 41, 150, 389, 377, 1, 3, 11, 41, 153, 533, 1187, 987, 1, 3, 11, 41, 153, 568, 1838, 3549, 2584, 1, 3, 11, 41, 153, 571, 2084, 6168, 10447, 6765, 1, 3, 11, 41, 153, 571, 2128
OFFSET
1,3
COMMENTS
Limiting row: A001835
Coefficient of x^n in v(n,x): even-indexed Fibonacci numbers
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*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...3
1...3...8
1...3...11...21
1...3...11...38...55
First three polynomials v(n,x): 1, 1 + 3x , 1 + 3x + 8x^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];
v[n_, x_] := 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[%] (* A209759 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209760 *)
CROSSREFS
Cf. A208510.
Sequence in context: A328807 A103279 A208910 * A046544 A011088 A352794
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 14 2012
STATUS
approved