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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A209750 Triangle of coefficients of polynomials v(n,x) jointly generated with A209749; see the Formula section. 3
1, 2, 1, 2, 4, 1, 3, 6, 7, 1, 3, 11, 15, 11, 1, 4, 14, 32, 32, 16, 1, 4, 21, 51, 79, 61, 22, 1, 5, 25, 84, 152, 174, 107, 29, 1, 5, 34, 118, 277, 393, 352, 176, 37, 1, 6, 39, 172, 447, 796, 915, 666, 275, 46, 1, 6, 50, 225, 705, 1446, 2060, 1965, 1193, 412, 56, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..66.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...1

2...4....1

3...6....7....1

3...11...15...11...1

MATHEMATICA

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

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

u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];

v[n_, x_] := u[n - 1, x] + 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[%]    (* A209749 *)

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

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

TableForm[cv]

Flatten[%]    (* A209750 *)

CROSSREFS

Cf. A209649, A208510.

Sequence in context: A165092 A306915 A270743 * A156042 A287691 A227926

Adjacent sequences:  A209747 A209748 A209749 * A209751 A209752 A209753

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 14 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 17 11:59 EDT 2019. Contains 328110 sequences. (Running on oeis4.)