OFFSET
0,4
COMMENTS
The number of compositions of n using elements from the set {1,3,5,7,9,10}.
Number of ways to tile an n-board (an n X 1 array of 1 X 1 cells) using squares, trominoes, pentominoes, heptominoes, nonominoes, and decominoes.
Number of permutations (p(1),p(2),...,p(n)) of (1,2,...,n) such that p(i)-i is in {-1,0,2,4,6,8,9} for all i=1,...,n.
a(n) gives the sums of the antidiagonals of A349841.
REFERENCES
D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), North-Holland, Amsterdam, 1970, pp. 755-770.
LINKS
V. Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics, 4(1) (2010), 119-135.
K. Edwards and M. A. Allen, Strongly restricted permutations and tiling with fences, Discrete Applied Mathematics, 187 (2015), 82-90.
Index entries for linear recurrences with constant coefficients, signature (1,0,1,0,1,0,1,0,1,1).
FORMULA
a(n) = a(n-1) + a(n-3) + a(n-5) + a(n-7) + a(n-9) + a(n-10) + delta(n,0), a(n<0)=0.
a(n) = a(n-1) + a(n-2) + a(n-10) - a(n-11) - a(n-12) + delta(n,0) - delta(n,2), a(n<0)=0.
G.f.: 1/(1-x-x^3-x^5-x^7-x^9-x^10).
MATHEMATICA
CoefficientList[Series[1/(1-x-x^3-x^5-x^7-x^9-x^10), {x, 0, 35}], x]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Michael A. Allen, Dec 13 2021
STATUS
approved