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A210556
Triangle of coefficients of polynomials v(n,x) jointly generated with A210555; see the Formula section.
3
1, 2, 2, 3, 4, 4, 4, 6, 10, 8, 5, 8, 18, 22, 16, 6, 10, 28, 42, 50, 32, 7, 12, 40, 68, 106, 110, 64, 8, 14, 54, 100, 188, 250, 242, 128, 9, 16, 70, 138, 300, 468, 594, 526, 256, 10, 18, 88, 182, 446, 780, 1188, 1378, 1138, 512, 11, 20, 108, 232, 630, 1202
OFFSET
1,2
COMMENTS
Alternating row sums: 1,0,3,0,9,0,27,0,81,0,...
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...2
3...4...4
4...6...10...8
5...8...18...22...16
First three polynomials v(n,x): 1, 2 + 2x , 3 + 4x + 4x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
v[n_, x_] := 2 x*u[n - 1, 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[%] (* A210555 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210556 *)
CROSSREFS
Sequence in context: A259197 A309559 A130128 * A208914 A049980 A359897
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 22 2012
STATUS
approved