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A210193 Triangle of coefficients of polynomials u(n,x) jointly generated with A210194; see the Formula section. 3
1, 3, 6, 3, 10, 14, 3, 15, 40, 23, 3, 21, 90, 97, 32, 3, 28, 175, 301, 181, 41, 3, 36, 308, 770, 728, 292, 50, 3, 45, 504, 1722, 2346, 1452, 430, 59, 3, 55, 780, 3486, 6456, 5686, 2554, 595, 68, 3, 66, 1155, 6534, 15774, 18722, 11816, 4115, 787, 77, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums:  powers of 3

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

LINKS

Table of n, a(n) for n=1..56.

FORMULA

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

v(n,x)=2x*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

6....3

10...14...3

15...40...23...3

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_] := 2 x*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[%]  (* A210193 *)

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

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

TableForm[cv]

Flatten[%]  (* A210194 *)

CROSSREFS

Cf. A210194, A208510.

Sequence in context: A129529 A298263 A128503 * A120906 A258758 A210201

Adjacent sequences:  A210190 A210191 A210192 * A210194 A210195 A210196

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Mar 18 2012

STATUS

approved

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Last modified October 16 16:18 EDT 2019. Contains 328101 sequences. (Running on oeis4.)