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A209758
Triangle of coefficients of polynomials v(n,x) jointly generated with A210041; see the Formula section.
3
1, 1, 3, 1, 5, 6, 1, 7, 13, 12, 1, 9, 22, 32, 24, 1, 11, 33, 63, 76, 48, 1, 13, 46, 107, 170, 176, 96, 1, 15, 61, 166, 321, 440, 400, 192, 1, 17, 78, 242, 546, 912, 1104, 896, 384, 1, 19, 97, 337, 864, 1683, 2488, 2704, 1984, 768, 1, 21, 118, 453, 1296, 2865
OFFSET
1,3
COMMENTS
Row sums: -1+(odd-indexed Fibonacci numbers)
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+v(n-1,x)+1,
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...5...6
1...7...13...12
1...9...22...32...24
First three polynomials v(n,x): 1, 1 + 3x , 1 + 5x + 6x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
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[%] (* A210041 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209758 *)
CROSSREFS
Sequence in context: A181641 A049266 A089028 * A134083 A210551 A113445
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 17 2012
STATUS
approved