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 A351873 #20 Mar 19 2025 08:26:58
%S A351873 1,2,4,8,12,16,21,29,45,73,117,178,260,376,552,832,1273,1945,2937,
%T A351873 4385,6521,9730,14612,22040,33252,50032,75053,112437,168549,253065,
%U A351873 380429,572018,859572,1290664,1937152,2907744,4366321,6558769,9853041,14800001,22226225
%N A351873 Number of subsets of {1,2,...,n} such that no two elements differ by 3 or 4.
%H A351873 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,1,2).
%H A351873 <a href="/index/Su#sublatts">Index entries for subsets of {1,..,n} with disallowed differences</a>
%F A351873 a(n) = a(n-1) + a(n-5) + a(n-6) + 2*a(n-7) + delta(n,0) + delta(n,1) + 2*delta(n,2) + 4*delta(n,3) + 4*delta(n,4) + 3*delta(n,5) + 2*delta(n,6).
%F A351873 G.f.: (1 + x + 2*x^2 + 4*x^3 + 4*x^4 + 3*x^5 + 2*x^6)/(1 - x - x^5 - x^6 - 2*x^7).
%e A351873 When n = 5, the 16 subsets are {}, {1}, {2}, {3}, {4}, {5}, {1,2}, {1,3}, {2,3}, {2,4}, {3,4}, {3,5}, {4,5}, {1,2,3}, {2,3,4}, and {3,4,5}.
%t A351873 CoefficientList[Series[(1 + x + 2x^2 + 4x^3 + 4x^4 + 3x^5 + 2x^6)/(1 - x - x^5 - x^6 - 2*x^7),{x,0,35}],x]
%t A351873 LinearRecurrence[{1,0,0,0,1,1,2},{1,2,4,8,12,16,21},50] (* _Harvey P. Dale_, Mar 01 2023 *)
%Y A351873 See A375981 for other sequences related to restricted combinations.
%Y A351873 Column k=12 of A376033.
%K A351873 easy,nonn
%O A351873 0,2
%A A351873 _Michael A. Allen_, Feb 22 2022