|
| |
|
|
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; 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.
|
|
|
FORMULA
| a(1)=1, a(2)=5, a(3)=16, a(n)= 3a(n-1) + 3a(n-2) - 3a(n-3).
|
|
|
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}]
|
|
|
CROSSREFS
| Sequence in context: A047103 A077235 A203232 * A203414 A189450 A180719
Adjacent sequences: A098344 A098345 A098346 * A098348 A098349 A098350
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 03 2004
|
| |
|
|
