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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}. 3
 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 Michael De Vlieger, Table of n, a(n) for n = 0..5708 Said Amrouche, HacĂ¨ne Belbachir, Unimodality and linear recurrences associated with rays in the Delannoy triangle, Turkish Journal of Mathematics (2019) Vol. 44, 118-130. 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 MATHEMATICA CoefficientList[Series[1/(1 - x - x^4 - x^5), {x, 0, 41}], x] (* Michael De Vlieger, Feb 03 2020 *) 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 March 29 03:09 EDT 2020. Contains 333104 sequences. (Running on oeis4.)