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A079962 Number of permutations satisfying -k <= p(i) - i <= r and p(i) - i not in I, i=1..n, with k=1, r=5, I={1,3}. 5
1, 1, 1, 2, 3, 5, 9, 14, 22, 36, 58, 94, 153, 247, 399, 646, 1045, 1691, 2737, 4428, 7164, 11592, 18756, 30348, 49105, 79453, 128557, 208010, 336567, 544577, 881145, 1425722, 2306866, 3732588, 6039454, 9772042, 15811497, 25583539, 41395035 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Number of compositions (ordered partitions) of n into elements of the set {1,3,5,6}. - Mark Dols, Aug 20 2010

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..38.

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 (1,0,1,0,1,1).

FORMULA

a(n) = a(n-1) + a(n-3) + a(n-5) + a(n-6).

G.f.: -1/((1+x+x^2)*(x^2-x+1)*(x^2+x-1)).

a(n+1)/a(n) -> golden ratio A001622. - Roger L. Bagula, Mar 13 2006

a(n) + a(n+2) + a(n+4) = Fibonacci(n+5). - Mark Dols, Aug 20 2010

a(n) = round(Fibonacci(n+3)/4). - Mircea Merca, Jan 04 2011

a(n+6) - a(n) = A000045(n+6). - Paul Curtz, Jun 29 2013

a(n) + a(n+1) + a(n+2) = A024490(n+6). - R. J. Mathar, Jun 30 2013

a(n) - a(n-1) + a(n-2) = A094686(n). - R. J. Mathar, Jun 30 2013

4*a(n) = A057078(n) + A010892(n) + A000045(n+3). - R. J. Mathar, Nov 02 2016

MAPLE

with(combinat, fibonacci): seq(round(fibonacci(n+3)/4), n=0..38) # Mircea Merca, Jan 04 2011

PROG

(PARI) a(n)=fibonacci(n+3)\/4 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

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

Sequence in context: A240841 A056686 A326332 * A244986 A293547 A124502

Adjacent sequences:  A079959 A079960 A079961 * A079963 A079964 A079965

KEYWORD

nonn,easy

AUTHOR

Vladimir Baltic, Feb 19 2003

STATUS

approved

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Last modified July 19 12:49 EDT 2019. Contains 325159 sequences. (Running on oeis4.)