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A210212
Triangle of coefficients of polynomials v(n,x) jointly generated with A210211; see the Formula section.
3
1, 2, 2, 3, 5, 4, 4, 10, 11, 8, 5, 16, 28, 23, 16, 6, 24, 51, 72, 47, 32, 7, 33, 90, 144, 176, 95, 64, 8, 44, 138, 294, 377, 416, 191, 128, 9, 56, 208, 492, 878, 938, 960, 383, 256, 10, 70, 290, 830, 1577, 2462, 2251, 2176, 767, 512, 11, 85, 400, 1250, 2952
OFFSET
1,2
COMMENTS
First and last terms of row n: n and 2^(n-1)
Alternating row sums are signed products of two Fibonacci numbers.
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)=u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...2
3...5...4
4...10...11...8
5...16...28...23...16
First three polynomials v(n,x): 1, 2 + 2x , 3 + 5x + 4x^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_] := 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[%] (* A210211 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210212 *)
CROSSREFS
Sequence in context: A282443 A210554 A208912 * A209762 A026408 A301790
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 19 2012
STATUS
approved