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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208511 Triangle of coefficients of polynomials u(n,x) jointly generated with A208512; see the Formula section. 3
1, 1, 1, 1, 3, 2, 1, 5, 7, 4, 1, 7, 14, 16, 8, 1, 9, 23, 37, 36, 16, 1, 11, 34, 69, 94, 80, 32, 1, 13, 47, 114, 195, 232, 176, 64, 1, 15, 62, 174, 354, 528, 560, 384, 128, 1, 17, 79, 251, 588, 1041, 1384, 1328, 832, 256, 1, 19, 98, 347, 916, 1863, 2938, 3536 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

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

FORMULA

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

v(n,x)=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...2

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

1...7...14...16...8

First five polynomials u(n,x):

1

1 + x

1 + 3x + 2x^2

1 + 5x + 7x^2 + 4x^3

1 + 7x + 14x^2 + 16x^3 + 8x^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_] := 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[%]  (* A208511 *)

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

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

TableForm[cv]

Flatten[%]  (* A208512 *)

CROSSREFS

Cf. A208511.

Sequence in context: A065366 A092879 A073370 * A129675 A232206 A209559

Adjacent sequences:  A208508 A208509 A208510 * A208512 A208513 A208514

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 28 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 21 04:26 EDT 2019. Contains 328291 sequences. (Running on oeis4.)