login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A210230 Triangle of coefficients of polynomials v(n,x) jointly generated with A210229; see the Formula section. 3
1, 3, 1, 6, 4, 1, 11, 11, 5, 1, 19, 26, 17, 6, 1, 32, 56, 48, 24, 7, 1, 53, 114, 121, 78, 32, 8, 1, 87, 223, 283, 223, 117, 41, 9, 1, 142, 424, 627, 584, 372, 166, 51, 10, 1, 231, 789, 1334, 1434, 1073, 579, 226, 62, 11, 1, 375, 1444, 2750, 3352, 2879, 1818 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums: 1,2,3,4,5,6,... (A000027)

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

LINKS

Table of n, a(n) for n=1..61.

FORMULA

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

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

where u(1,x)=1, v(1,x)=1.

EXAMPLE

First five rows:

1

3....1

6....4....1

11...11...5....1

19...26...17...6...1

First three polynomials v(n,x): 1, 3 + x , 6 + 4x + x^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_] := (x + 1)*u[n - 1, 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[%]     (* A210229 *)

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

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

TableForm[cv]

Flatten[%]     (* A210230 *)

CROSSREFS

Cf. A210229, A208510.

Sequence in context: A108286 A185944 A131415 * A207615 A209165 A121437

Adjacent sequences:  A210227 A210228 A210229 * A210231 A210232 A210233

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 20 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 18:50 EDT 2019. Contains 328319 sequences. (Running on oeis4.)