A349843 - OEIS

%I #11 Dec 22 2021 10:20:08

%S 1,1,1,2,3,5,8,13,21,34,56,90,145,235,380,615,995,1610,2605,4215,6821,

%T 11036,17856,28892,46748,75640,122388,198028,320416,518444,838861,

%U 1357305,2196165,3553470,5749635,9303105

%N Expansion of (1 - x^2)/((1 - x^10)(1 - x - x^2)).

%C The number of compositions of n using elements from the set {1,3,5,7,9,10}.

%C 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.

%C 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.

%C a(n) gives the sums of the antidiagonals of A349841.

%D 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.

%H V. Baltic, <a href="http://pefmath.etf.rs/vol4num1/AADM-Vol4-No1-119-135.pdf">On the number of certain types of strongly restricted  permutations</a>, Applicable Analysis and Discrete Mathematics, 4(1) (2010), 119-135.

%H K. Edwards and M. A. Allen, <a href="http://dx.doi.org/10.1016/j.dam.2015.02.004">Strongly restricted permutations and tiling with fences</a>, Discrete Applied Mathematics, 187 (2015), 82-90.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,0,1,0,1,0,1,1).

%F 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.

%F 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.

%F G.f.: 1/(1-x-x^3-x^5-x^7-x^9-x^10).

%t CoefficientList[Series[1/(1-x-x^3-x^5-x^7-x^9-x^10), {x, 0, 35}], x]

%Y Sums of antidiagonals of triangles in the same family as A349841: A000045, A006498, A079962, A349840.

%K easy,nonn

%O 0,4

%A _Michael A. Allen_, Dec 13 2021