login
A210195
Triangle of coefficients of polynomials u(n,x) jointly generated with A210196; see the Formula section.
3
1, 3, 5, 4, 7, 12, 8, 9, 24, 32, 16, 11, 40, 80, 80, 32, 13, 60, 160, 240, 192, 64, 15, 84, 280, 560, 672, 448, 128, 17, 112, 448, 1120, 1792, 1792, 1024, 256, 19, 144, 672, 2016, 4032, 5376, 4608, 2304, 512, 21, 180, 960, 3360, 8064, 13440, 15360
OFFSET
1,2
COMMENTS
Row sums: powers of 3
Periodic alternating row sums: 1,3,1,3,1,3,1,3,...
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+v(n-1,x)+1,
v(n,x)=2x*u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
3
5...4
7...12...8
9...24...32...16
First three polynomials u(n,x): 1, 3, 5 + 4x.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := 2 x*u[n - 1, x] + 2 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[%] (* A210195 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210196 *)
CROSSREFS
Sequence in context: A277897 A082568 A242640 * A069918 A361709 A200700
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Mar 18 2012
STATUS
approved