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 A375985 #13 Mar 19 2025 08:38:31
%S A375985 1,2,3,5,7,9,11,14,18,25,35,49,67,90,119,158,211,285,387,526,712,960,
%T A375985 1290,1733,2331,3142,4241,5727,7729,10422,14043,18918,25490,34359,
%U A375985 46329,62478,84250,113590,153123,206400,278219,375056,505635,681703,919076,1239066
%N A375985 Number of subsets of {1,2,...,n} such that no two elements differ by 1, 3, 4, or 5.
%C A375985 a(n) is the number of compositions of n+5 into parts 1, 6, and 8.
%H A375985 Michael A. Allen, <a href="https://doi.org/10.22049/CCO.2024.29370.1959">Combinations without specified separations</a>, Communications in Combinatorics and Optimization (in press).
%H A375985 Michael A. Allen, <a href="https://doi.org/10.48550/arXiv.2409.00624">Connections between Combinations Without Specified Separations and Strongly Restricted Permutations, Compositions, and Bit Strings</a>, arXiv:2409.00624 [math.CO], 2024.
%H A375985 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,0,1).
%H A375985 <a href="/index/Su#sublatts">Index entries for subsets of {1,..,n} with disallowed differences</a>
%F A375985 a(n) = a(n-1) + a(n-6) + a(n-8) for n >= 8.
%F A375985 G.f.: (1 + x + x^2 + 2*x^3 + 2*x^4 + 2*x^5 + x^6 + x^7)/((1 + x)(1 - 2*x + 2*x^2 - 2*x^3 + 2*x^4 - 2*x^5 + x^6 - x^7)).
%e A375985 For n = 6, the 11 subsets are {}, {1}, {2}, {3}, {1,3}, {4}, {2,4}, {5}, {3,5}, {6}, {4,6}.
%t A375985 CoefficientList[Series[(1 + x + x^2 + 2*x^3 + 2*x^4 + 2*x^5 + x^6 + x^7)/(1 - x - x^6 - x^8),{x,0,43}],x]
%t A375985 LinearRecurrence[{1, 0, 0, 0, 0, 1, 0, 1}, {1, 2, 3, 5, 7, 9, 11, 14}, 44]
%Y A375985 Column k=29 of A376033.
%K A375985 easy,nonn
%O A375985 0,2
%A A375985 _Michael A. Allen_, Sep 21 2024