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A210228 Triangle of coefficients of polynomials v(n,x) jointly generated with A210227; see the Formula section. 3
1, 1, 4, 1, 6, 10, 1, 6, 24, 22, 1, 6, 28, 80, 46, 1, 6, 28, 120, 236, 94, 1, 6, 28, 128, 464, 640, 190, 1, 6, 28, 128, 568, 1624, 1636, 382, 1, 6, 28, 128, 584, 2376, 5224, 4008, 766, 1, 6, 28, 128, 584, 2632, 9240, 15696, 9516, 1534, 1, 6, 28, 128, 584 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Table of n, a(n) for n=1..60.

FORMULA

u(n,x)=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

1...4

1...6...10

1...6...24...22

1...6...28...80...46

First three polynomials v(n,x): 1, 1 + 4x , 1 + 6x + 19x^2.

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := 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[%]     (* A210227 *)

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

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

TableForm[cv]

Flatten[%]     (* A210228 *)

CROSSREFS

Cf. A210227, A208510.

Sequence in context: A154905 A124739 A122662 * A209161 A083843 A094264

Adjacent sequences:  A210225 A210226 A210227 * A210229 A210230 A210231

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 20 2012

STATUS

approved

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Last modified October 18 08:00 EDT 2019. Contains 328146 sequences. (Running on oeis4.)