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A351874 Number of subsets of {1,2,...,n} such that no two elements differ by 1, 3, or 4.

%I A351874 #19 Mar 19 2025 08:31:39
%S A351874 1,2,3,5,7,9,12,16,23,33,47,66,91,126,175,245,344,482,674,940,1311,
%T A351874 1830,2557,3575,4997,6982,9752,13620,19025,26579,37136,51885,72487,
%U A351874 101264,141463,197624,276088,385711,538860,752810,1051698,1469249,2052584,2867532
%N A351874 Number of subsets of {1,2,...,n} such that no two elements differ by 1, 3, or 4.
%H A351874 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,0,1).
%H A351874 <a href="/index/Su#sublatts">Index entries for subsets of {1,..,n} with disallowed differences</a>
%F A351874 a(n) = a(n-1) + a(n-5) + a(n-7) + delta(n,0) + delta(n,1) + delta(n,2) + 2*delta(n,3) + 2*delta(n,4) + delta(n,5) + delta(n,6), a(n<0) = 0.
%F A351874 G.f.: (1 + x + x^2 + 2*x^3 + 2*x^4 + x^5 + x^6)/(1 - x - x^5 - x^7).
%e A351874 When n = 5, the 9 subsets are {}, {1}, {2}, {3}, {4}, {5}, {1,3}, {2,4}, and {3,5}.
%t A351874 CoefficientList[Series[(1 + x + x^2 + 2x^3 + 2x^4 + x^5 + x^6)/(1 - x - x^5 - x^7),{x,0,45}],x]
%Y A351874 Column k=13 of A376033.
%K A351874 easy,nonn
%O A351874 0,2
%A A351874 _Michael A. Allen_, Feb 22 2022