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 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 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

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