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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208610 Triangle of coefficients of polynomials u(n,x) jointly generated with A208611; see the Formula section. 3
1, 1, 1, 1, 3, 3, 1, 5, 9, 7, 1, 7, 17, 25, 17, 1, 9, 27, 55, 69, 41, 1, 11, 39, 99, 171, 187, 99, 1, 13, 53, 159, 341, 515, 501, 239, 1, 15, 69, 237, 599, 1125, 1515, 1329, 577, 1, 17, 87, 335, 967, 2141, 3591, 4373, 3497, 1393, 1, 19, 107, 455, 1469, 3713 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

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

FORMULA

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

v(n,x)=(x+1)*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...1

1...3...3

1...5...9...7

1...7...17...25...17

First five polynomials u(n,x):

1

1 + x

1 + 3x + 3x^2

1 + 5x + 9x^2 + 7x^3

1 + 7x + 17x^2 + 25x^3 + 17x^4

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*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[%]  (* A208610 *)

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

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

TableForm[cv]

Flatten[%]  (* A208611 *)

CROSSREFS

Cf. A208611.

Sequence in context: A272295 A164984 A248810 * A193823 A071945 A209583

Adjacent sequences:  A208607 A208608 A208609 * A208611 A208612 A208613

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 01 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 February 16 08:26 EST 2019. Contains 320159 sequences. (Running on oeis4.)