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A210201 Triangle of coefficients of polynomials u(n,x) jointly generated with A210202; see the Formula section. 3
1, 3, 6, 3, 11, 10, 6, 19, 27, 23, 12, 32, 62, 73, 52, 24, 53, 132, 193, 187, 116, 48, 87, 266, 468, 552, 462, 256, 96, 142, 517, 1061, 1482, 1495, 1112, 560, 192, 231, 978, 2297, 3688, 4369, 3896, 2624, 1216, 384, 375, 1813, 4797, 8703, 11758 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums:  3^(n-1)

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..51.

FORMULA

u(n,x)=u(n-1,x)+v(n-1,x)+1,

v(n,x)=(x+1)*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

6....3

11...10...6

19...27...23...12

First three polynomials u(n,x): 1, 3, 6 + 3x.

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_] := (x + 1)*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[%]   (* A210201 *)

Table[Expand[v[n, x]], {n, 1, z}]

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%]   (* A210202 *)

CROSSREFS

Cf. A210202, A208510.

Sequence in context: A210193 A120906 A258758 * A275535 A160899 A203491

Adjacent sequences:  A210198 A210199 A210200 * A210202 A210203 A210204

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Mar 18 2012

STATUS

approved

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Last modified October 16 16:13 EDT 2019. Contains 328101 sequences. (Running on oeis4.)