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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A098347 A sequence derived from a Ferrers graph partition of 16. 0
1, 5, 16, 60, 213, 771, 2772, 9990, 35973, 129573, 466668, 1680804, 6053697, 21803499, 78529176, 282836934, 1018687833, 3668986773, 13214513016, 47594435868, 171419886333, 617399427555, 2223674634060, 8008962525846 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

One of the partitions of 16 is 5+5+2+2+1. Convert this Ferrers graph representation to a 5 X 5 binary matrix.

Lim_{n->inf.} = 3.60167913188315425246437..., the characteristic polynomial of m & m^-1 is x^5-3x^4-3x^3+3x^2 and its only positive root is the limit.

LINKS

Table of n, a(n) for n=1..24.

Index entries for linear recurrences with constant coefficients, signature (3,3,-3).

FORMULA

a(1)=1, a(2)=5, a(3)=16, a(n)= 3a(n-1) + 3a(n-2) - 3a(n-3).

G.f.: -x*(2*x^2-2*x-1) / (3*x^3-3*x^2-3*x+1). - Colin Barker, Oct 19 2013

EXAMPLE

a(4)=60 because m^4.{1,0,0,0,0} = {60, 60, 45, 32, 16} and the first or second element is 60.

MATHEMATICA

a[1] = 1; a[2] = 5; a[3] = 16; a[n_] := a[n] = 3a[n - 1] + 3a[n - 2] - 3a[n - 3]; Table[ a[n], {n, 24}] (* Or *)

m = {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 0, 0}, {1, 1, 0, 0, 0}, {1, 0, 0, 0, 0}}; Table[(MatrixPower[m, n].{1, 0, 0, 0, 0})[[1]], {n, 24}]

PROG

(PARI) Vec(-x*(2*x^2-2*x-1)/(3*x^3-3*x^2-3*x+1) + O(x^100)) \\ Colin Barker, Oct 19 2013

CROSSREFS

Sequence in context: A226897 A077235 A203232 * A203414 A189450 A180719

Adjacent sequences:  A098344 A098345 A098346 * A098348 A098349 A098350

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson and Robert G. Wilson v, Sep 03 2004

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 September 16 12:41 EDT 2019. Contains 327113 sequences. (Running on oeis4.)