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A210597
Triangle of coefficients of polynomials u(n,x) jointly generated with A210602; see the Formula section.
3
1, 2, 2, 4, 5, 4, 7, 13, 12, 8, 12, 28, 37, 28, 16, 20, 58, 92, 98, 64, 32, 33, 114, 217, 273, 248, 144, 64, 54, 218, 479, 713, 760, 608, 320, 128, 88, 407, 1018, 1727, 2161, 2024, 1456, 704, 256, 143, 747, 2093, 3997, 5662, 6194, 5216, 3424, 1536, 512
OFFSET
1,2
COMMENTS
Row n starts with F(n+2)-1, where F=A000045 (Fibonacci
numbers), and ends with 2^(n-1). For a discussion and
guide to related arrays, see A208510.
FORMULA
u(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
v(n,x)=(x+1)*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
4....5....4
7....13...12...8
12...28...37...28...16
First three polynomials u(n,x): 1, 2+ 2x, 4 + 5x + 4x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*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[%] (* A210597 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210602 *)
CROSSREFS
Sequence in context: A202876 A128900 A136099 * A252836 A286101 A072454
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 24 2012
STATUS
approved