This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A349840 #24 Aug 18 2025 06:28:22
%S A349840 1,1,1,2,3,5,8,13,22,35,56,91,147,238,385,623,1009,1632,2640,4272,
%T A349840 6912,11184,18096,29280,47377,76657,124033,200690,324723,525413,
%U A349840 850136,1375549,2225686,3601235,5826920,9428155
%N A349840 The number of compositions of n using elements from the set {1,3,5,7,8}.
%C A349840 Number of ways to tile an n-board (an n X 1 array of 1 X 1 cells) using squares, trominoes, pentominoes, heptominoes, and octominoes.
%C A349840 Number of permutations (p(1),p(2),...,p(n)) of (1,2,...,n) such that p(i)-i is in {-1,0,2,4,6,7} for all i=1,...,n.
%C A349840 a(n) gives the sums of the antidiagonals of A349839.
%D A349840 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 A349840 Vladimir 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 A349840 K. Edwards and Michael 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 A349840 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,0,1,0,1,1).
%F A349840 a(n) = a(n-1) + a(n-3) + a(n-5) + a(n-7) + a(n-8) + delta(n,0), a(n<0)=0 (where delta(i,j) is the Kronecker delta).
%F A349840 a(n) = a(n-1) + a(n-2) + a(n-8) - a(n-9) - a(n-10) + delta(n,0) - delta(n,2), a(n<0)=0.
%F A349840 G.f.: 1/(1-x-x^3-x^5-x^7-x^8).
%t A349840 CoefficientList[Series[1/(1-x-x^3-x^5-x^7-x^8),{x,0,35}],x]
%Y A349840 Sums of antidiagonals of triangles in the same family as A349839: A000045, A006498, A079962, A349843.
%K A349840 easy,nonn
%O A349840 0,4
%A A349840 _Michael A. Allen_, Dec 05 2021