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A210742
Triangle of coefficients of polynomials v(n,x) jointly generated with A210741; see the Formula section.
3
1, 3, 2, 5, 9, 5, 7, 20, 27, 13, 9, 35, 73, 80, 34, 11, 54, 151, 252, 234, 89, 13, 77, 269, 597, 837, 677, 233, 15, 104, 435, 1199, 2225, 2702, 1941, 610, 17, 135, 657, 2158, 4956, 7943, 8533, 5523, 1597, 19, 170, 943, 3590, 9796, 19387, 27435, 26479
OFFSET
1,2
COMMENTS
Row n starts with 2n-1 and ends with an odd-indexed
Fibonacci number.
Row sums: A035344
Alternate row sums: 1,1,1,1,1,1,1,1,...
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
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
3...2
5...9....5
7...20...27...13
9...35...73...80...34
First three polynomials v(n,x): 1, 3 + 2x, 5 + 9x + 5x^2
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;
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[%] (* A210741 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210742 *)
CROSSREFS
Sequence in context: A173701 A116627 A254331 * A175056 A320274 A333398
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 24 2012
STATUS
approved