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A209170
Triangle of coefficients of polynomials u(n,x) jointly generated with A209171; see the Formula section.
3
1, 2, 1, 5, 6, 2, 11, 20, 13, 3, 23, 57, 57, 27, 5, 47, 149, 202, 144, 53, 8, 95, 369, 633, 604, 334, 101, 13, 191, 881, 1831, 2192, 1618, 733, 188, 21, 383, 2049, 5007, 7217, 6665, 4022, 1544, 344, 34, 767, 4673, 13135, 22153, 24570, 18519, 9461
OFFSET
1,2
COMMENTS
Row n ends with A000045 (Fibonacci numbers).
Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,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
2....1
5....6....2
11...20...13...3
23...57...57...27...5
First three polynomials v(n,x): 1, 2 + x, 5 + 6x + 2x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, 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;
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[%] (* A209170 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209171 *)
CROSSREFS
Sequence in context: A342968 A323312 A231774 * A231732 A185384 A274728
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 08 2012
STATUS
approved