|
Search: id:A007482
|
|
|
| A007482 |
|
Number of subsequences of [ 1,...,2n ] in which each odd number has an even neighbor.
(Formerly M2893)
|
|
+0
16
|
|
| 1, 3, 11, 39, 139, 495, 1763, 6279, 22363, 79647, 283667, 1010295, 3598219, 12815247, 45642179, 162557031, 578955451, 2061980415, 7343852147, 26155517271, 93154256107, 331773802863, 1181629920803, 4208437368135
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
The even neighbor must differ from the odd number by exactly one.
If we defined this sequence by the recurrence (a(n) = 3*a(n-1) + 2*a(n-2)) that it satisfies, we could prefix it with an initial 0.
|
|
REFERENCES
|
R. K. Guy, Moser, William O.J.: Numbers of subsequences without isolated odd members. Fibonacci Quarterly, 34, No. 2, 152-155 (1996). Math. Rev. 97d:11017.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..200
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 442
|
|
FORMULA
|
Let b(0)=1, b(k)=floor(b(k-1))+2/b(k-1); then, for n>0, b(n)=a(n)/a(n-1). - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 09 2002
The Hankel transform of this sequence is [1,2,0,0,0,0,0,0,0,...]. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2007
G.f.: 1/(1-3x-2x^2). a(n)=3a(n-1)+2a(n-2). a(n)=(ap^(n+1)-am^(n+1))/(ap-am), ap := (3+sqrt(17))/2, am := (3-sqrt(17))/2.
a(n)=sum{k=0..floor(n/2), C(n-k, k)2^k*3^(n-2k)} - Paul Barry (pbarry(AT)wit.ie), Apr 23 2005
a(n)=Sum_{k, 0<=k<=n}A112906(n,k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2007
|
|
CROSSREFS
|
Cf. A007455, A007481, A007483, A007484.
Row sums of triangle A073387.
Cf. A000045, A000129, A001045.
Sequence in context: A064086 A089579 A002783 this_sequence A134760 A132889 A066979
Adjacent sequences: A007479 A007480 A007481 this_sequence A007483 A007484 A007485
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
njas
|
|
|
Search completed in 0.002 seconds
|
