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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208608 Triangle of coefficients of polynomials u(n,x) jointly generated with A208609; see the Formula section. 3
1, 1, 1, 1, 3, 2, 1, 5, 6, 3, 1, 7, 12, 12, 5, 1, 9, 20, 29, 23, 8, 1, 11, 30, 56, 64, 43, 13, 1, 13, 42, 95, 140, 136, 79, 21, 1, 15, 56, 148, 265, 332, 279, 143, 34, 1, 17, 72, 217, 455, 692, 751, 558, 256, 55, 1, 19, 90, 304, 728, 1295, 1708, 1641, 1093, 454 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

coefficient of x^(n-1)=Fibonacci(n)=A000045(n)

LINKS

Table of n, a(n) for n=1..65.

FORMULA

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

v(n,x)=(x+1)*u(n-1,x)+x*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...6....3

1...7...12...12...5

First five polynomials u(n,x):

1

1 + x

1 + 3x + 2x^2

1 + 5x + 6x^2 + 3x^3

1 + 7x + 12x^2 + 12x^3 + 5x^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] + 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[%]  (* A208608 *)

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

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

TableForm[cv]

Flatten[%]  (* A208609 *)

CROSSREFS

Cf. A208609.

Sequence in context: A132969 A132970 A192022 * A209577 A139377 A138483

Adjacent sequences:  A208605 A208606 A208607 * A208609 A208610 A208611

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 29 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 3 12:51 EST 2016. Contains 278737 sequences.