A079961 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={1,4}.

1, 1, 1, 2, 4, 6, 10, 17, 28, 46, 77, 128, 212, 352, 585, 971, 1612, 2677, 4445, 7380, 12254, 20347, 33784, 56095, 93141, 154652, 256785, 426368, 707945, 1175477, 1951771, 3240736, 5380943, 8934559, 14835011, 24632167, 40899440, 67909746

Offset: 0

Author

Vladimir Baltic, Feb 19 2003

Keywords

• nonn
• easy

Comments

Number of compositions (ordered partitions) of n into elements of the set {1,3,4,6}.

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

• 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 (1,0,1,1,0,1).

Crossrefs

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

Programs

Maple

g:=1/(1-z-z^3-z^4-z^6): gser:=series(g, z=0, 49): seq((coeff(gser, z, n)), n=0..37); # Zerinvary Lajos, Apr 17 2009

Formula

a(n) = a(n-1)+a(n-3)+a(n-4)+a(n-6).

G.f.: -1/(x^6+x^4+x^3+x-1).