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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A209562 Triangle of coefficients of polynomials v(n,x) jointly generated with A209561; see the Formula section. 3
1, 2, 1, 3, 2, 1, 4, 4, 3, 1, 5, 7, 7, 4, 1, 6, 11, 14, 11, 5, 1, 7, 16, 25, 25, 16, 6, 1, 8, 22, 41, 50, 41, 22, 7, 1, 9, 29, 63, 91, 91, 63, 29, 8, 1, 10, 37, 92, 154, 182, 154, 92, 37, 9, 1, 11, 46, 129, 246, 336, 336, 246, 129, 46, 10, 1, 12, 56, 175, 375, 582, 672 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums: 1,1,2,2,2,2,2,2,2,2,2,2,2,2,...

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

LINKS

Table of n, a(n) for n=1..72.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...1

3...2...1

4...4...3...1

5...7...7...4...1

First three polynomials v(n,x): 1, 3 + x , 5 + 5x + 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];

v[n_, x_] := x*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[%]   (* A209561 *)

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

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

TableForm[cv]

Flatten[%]   (* A209562 *)

CROSSREFS

Cf. A209561, A208510.

Sequence in context: A105438 A062001 A181847 * A259344 A239030 A165999

Adjacent sequences:  A209559 A209560 A209561 * A209563 A209564 A209565

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 10 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 14:44 EDT 2019. Contains 328318 sequences. (Running on oeis4.)