_Clark Kimberling (ck6(AT)evansville.edu), _, Mar 18 2012

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allocated for Clark KimberlingTriangle of coefficients of polynomials u(n,x) jointly generated with A210196; see the Formula section.

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

1,2

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.

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.

First five rows:

1

3

5...4

7...12...8

9...24...32...16

First three polynomials u(n,x): 1, 3, 5 + 4x.

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 *)

Cf. A210196, A208510.

allocated

nonn,tabf

Clark Kimberling (ck6(AT)evansville.edu), Mar 18 2012

approved

editing

allocated for Clark Kimberling

allocated

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