|
Search: id:A055841
|
|
|
| A055841 |
|
A second order recursive sequence. |
|
+0
3
|
|
| 1, 2, 9, 36, 144, 576, 2304, 9216, 36864, 147456, 589824, 2359296, 9437184, 37748736, 150994944, 603979776, 2415919104, 9663676416, 38654705664, 154618822656, 618475290624, 2473901162496
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
First differences of A002001.
For n>=2, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4} such that for fixed, different x_1, x_2 in {1,2,...,n} and fixed y_1, y_2 in {1,2,3,4} we have f(x_1)<>y_1 and f(x_2)<> y_2. - Milan R. Janjic (agnus(AT)blic.net), Apr 19 2007
|
|
REFERENCES
|
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pps. 194-196.
|
|
LINKS
|
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
|
|
FORMULA
|
a(n)=9*4^(n-2), a(0)=1, a(1)=2.
|
|
EXAMPLE
|
a(n)=4a(n-1)+[(-1)^n]*C(2,2-n). G.f.(x)=(1-x)^2/(1-4x).
|
|
CROSSREFS
|
Cf. A000302 and A002001.
Essentially the same as A002063.
Sequence in context: A027995 A077836 A003125 this_sequence A037521 A037730 A029874
Adjacent sequences: A055838 A055839 A055840 this_sequence A055842 A055843 A055844
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Barry E. Williams, May 30 2000
|
|
|
Search completed in 0.002 seconds
|
