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 A375981 #20 Mar 19 2025 08:22:12
%S A375981 1,2,3,5,8,11,14,19,25,34,49,70,99,141,196,270,375,520,723,1014,1420,
%T A375981 1985,2777,3874,5396,7526,10496,14642,20449,28555,39860,55647,77660,
%U A375981 108356,151214,211028,294507,411071,573763,800796,1117679,1559895,2177002
%N A375981 Number of subsets of {1,2,...,n} such that no two elements differ by 1, 4, or 5.
%C A375981 a(n) is the number of compositions of n+5 into parts 1, 6, 8, 9, 12, 15, 18, 21, ...
%H A375981 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 A375981 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 A375981 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1,0,1,0,1,0,0,-1).
%H A375981 <a href="/index/Su#sublatts">Index entries for subsets of {1,..,n} with disallowed differences</a>
%F A375981 a(n) = a(n-1) + a(n-3) - a(n-4) + a(n-6) + a(n-8) - a(n-11) for n >= 11.
%F A375981 G.f.: (1 + x + x^2 + x^3 + 2*x^4 + 2*x^5 - x^8 - x^9 - x^10)/(1 - x - x^3 + x^4 - x^6 - x^8 + x^11).
%e A375981 For n = 6, the 14 subsets are {}, {1}, {2}, {3}, {1,3}, {4}, {1,4}, {2,4}, {5}, {2,5}, {3,5}, {6}, {3,6}, {4,6}.
%e A375981 The a(4) = 8 compositions of 9 into parts 1, 6, 8, 9, ... are 1+1+1+1+1+1+1+1+1, 1+1+1+6, 1+1+6+1, 1+6+1+1, 6+1+1+1, 1+8, 8+1, 9.
%t A375981 CoefficientList[Series[(1 + x + x^2 + x^3 + 2*x^4 + 2*x^5 - x^8 - x^9 - x^10)/(1 - x - x^3 + x^4 - x^6 - x^8 + x^11),{x,0,42}],x]
%t A375981 LinearRecurrence[{1, 0, 1, -1, 0, 1, 0, 1, 0, 0, -1}, {1, 2, 3, 5, 8, 11, 14, 19, 25, 34, 49}, 42]
%Y A375981 See comments for other sequences related to restricted combinations.
%Y A375981 Cf. A376743.
%K A375981 easy,nonn
%O A375981 0,2
%A A375981 _Michael A. Allen_, Sep 04 2024