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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A209578 Triangle of coefficients of polynomials v(n,x) jointly generated with A209577; see the Formula section. 3
1, 3, 1, 5, 3, 1, 9, 8, 4, 1, 15, 19, 13, 5, 1, 25, 41, 36, 19, 6, 1, 41, 84, 90, 60, 26, 7, 1, 67, 165, 210, 169, 92, 34, 8, 1, 109, 315, 465, 439, 287, 133, 43, 9, 1, 177, 588, 990, 1073, 818, 454, 184, 53, 10, 1, 287, 1079, 2043, 2502, 2178, 1405, 681, 246 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums: 1,0,2,1,3,2,4,3,5,4,... (A028242).

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

LINKS

Table of n, a(n) for n=1..63.

FORMULA

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

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

1...1

3...2....1

5...6....3....1

9...13...10...4...1

First three polynomials v(n,x): 1, 1 + x , 3 + 2x + 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 + 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[%]   (* A209577 *)

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

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

TableForm[cv]

Flatten[%]   (* A209578 *)

CROSSREFS

Cf. A209577, A208510.

Sequence in context: A060439 A206283 A135224 * A268829 A249100 A152203

Adjacent sequences:  A209575 A209576 A209577 * A209579 A209580 A209581

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 11 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 15 10:46 EDT 2019. Contains 328026 sequences. (Running on oeis4.)