|
| |
|
|
A079028
|
|
a(0) = 1, a(n) = (n+4)*4^(n-1) for n >= 1.
|
|
6
|
|
|
|
1, 5, 24, 112, 512, 2304, 10240, 45056, 196608, 851968, 3670016, 15728640, 67108864, 285212672, 1207959552, 5100273664, 21474836480, 90194313216, 377957122048, 1580547964928, 6597069766656, 27487790694400
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
a(n) = det(M(n)) where M(n) is the n X n matrix defined by m(i,i) = 5, m(i,j) = i/j.
Main diagonal of array defined by m(1,j)=j; m(i,1)=i and m(i,j)=m(i-1,j)+3*m(i-1,j-1).
4th binomial transform of (1,1,0,0,0,0,.....). - Paul Barry, Mar 07 2003
Number of independent vertex subsets of the graph obtained by attaching two pendant edges to each vertex of the complete graph K_n (see A235113). Example: a(1)=5; indeed, K_1 is the one vertex graph and after attaching two pendant vertices we obtain the path graph ABC; the independent vertex subsets are: empty, {A}, {B}, {C}, and {A,C}. [Emeric Deutsch, Jan 13 2014]
Row sums of A235113.
|
|
|
LINKS
|
Table of n, a(n) for n=0..21.
F. Disanto, A. Frosini, R. Pinzani and S. Rinaldi, A closed formula for the number of convex permutominoes, arXiv:math/0702550 [math.CO], 2007.
|
|
|
FORMULA
|
a(n) = 8*a(n-1)-16*a(n-2), a(0) = 1, a(1) = 5. - Paul Barry, Mar 07 2003
a(n) = (1/4)*(n-1)*4^(n-1)+4^(n-1), with n>=1. - Paolo P. Lava, Jul 08 2008
G.f.: (1-3*x)/(1-4*x)^2 . - Philippe Deléham, Dec 11 2008
From Amiram Eldar, Jan 14 2021: (Start)
Sum_{n>=0} 1/a(n) = 1024*log(4/3) - 880/3.
Sum_{n>=0} (-1)^n/a(n) = 688/3 - 1024*log(5/4). (End)
|
|
|
MATHEMATICA
|
LinearRecurrence[{8, -16}, {1, 5}, 22] (* Jean-François Alcover, Nov 06 2018 *)
|
|
|
PROG
|
(Sage) [lucas_number2(n, 4, 0)*n/2^10 for n in range(4, 26)] # Zerinvary Lajos, Mar 13 2009
|
|
|
CROSSREFS
|
Cf. A001792, A006234, A081105, A006234, A235113.
Cf. A002697, A034007, A079861, A045891, A087449.
Sequence in context: A225116 A296770 A081104 * A218987 A272257 A347029
Adjacent sequences: A079025 A079026 A079027 * A079029 A079030 A079031
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Benoit Cloitre, Feb 01 2003
|
|
|
STATUS
|
approved
|
| |
|
|
