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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A079972 Number of permutations satisfying -k <= p(i)-i <= r and p(i)-i not in I, i=1..n, with k=1, r=4, I={1,2}. 2
1, 1, 1, 1, 2, 4, 6, 8, 11, 17, 27, 41, 60, 88, 132, 200, 301, 449, 669, 1001, 1502, 2252, 3370, 5040, 7543, 11297, 16919, 25329, 37912, 56752, 84968, 127216, 190457, 285121, 426841, 639025, 956698, 1432276, 2144238, 3210104, 4805827, 7194801 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Number of compositions (ordered partitions) of n into elements of the set {1,4,5}.

a(n+3) is the number of length-n binary words with no substring 1x1 of 1xy1 (that is, no 1's occur with distance two or three), see fxtbook link. - Joerg Arndt, May 27 2011

REFERENCES

D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.

LINKS

Table of n, a(n) for n=0..41.

Joerg Arndt, Matters Computational (The Fxtbook), section 14.10.3, p. 322

Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,1).

FORMULA

a(n) = a(n-1) + a(n-4) + a(n-5).

G.f.: 1/(1-x-x^4-x^5).

a(n) = Sum_{k=0..n} Sum_{j=floor((n-k)/4)..floor((n-k)/3)} binomial(k,j)*binomial(j,n-k-3*j). - Vladimir Kruchinin, May 26 2011

PROG

(Maxima)

a(n):=sum(sum(binomial(k, j)*binomial(j, n-k-3*j), j, floor((n-k)/4), floor((n-k)/3)), k, 0, n); /* Vladimir Kruchinin, May 26 2011 */

CROSSREFS

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.

Sequence in context: A213609 A039823 A284617 * A164144 A071241 A247123

Adjacent sequences:  A079969 A079970 A079971 * A079973 A079974 A079975

KEYWORD

nonn

AUTHOR

Vladimir Baltic, Feb 17 2003

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 January 17 22:51 EST 2019. Contains 319251 sequences. (Running on oeis4.)