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A210600
Triangle of coefficients of polynomials u(n,x) jointly generated with A210601; see the Formula section.
3
1, 2, 2, 4, 7, 4, 7, 19, 20, 8, 12, 44, 69, 52, 16, 20, 94, 196, 218, 128, 32, 33, 190, 497, 731, 632, 304, 64, 54, 370, 1167, 2139, 2440, 1728, 704, 128, 88, 701, 2594, 5701, 8081, 7544, 4528, 1600, 256, 143, 1301, 5533, 14195, 24062, 27874, 22048
OFFSET
1,2
COMMENTS
Alternating row sums: 1,0,1,0,1,0,1,0,...
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=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....2
4....7....4
7....19...20...8
12...44...69...52...16
First three polynomials u(n,x): 1, 2+ 2x, 4 + 7x + 4x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*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[%] (* A210600 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210601 *)
CROSSREFS
Sequence in context: A209142 A368518 A115754 * A220308 A203975 A270246
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 24 2012
STATUS
approved