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%I A375186 #14 Oct 03 2024 15:14:13
%S A375186 1,2,3,4,6,8,10,14,19,25,35,48,64,88,120,161,220,300,405,552,752,1018,
%T A375186 1385,1885,2556,3475,4727,6416,8720,11857,16102,21881,29745,40406,
%U A375186 54905,74626,101389,137769,187235,254404,345689,469781,638339
%N A375186 Number of subsets of {1,2,...,n} such that no two elements differ by 1, 2, 4, or 5.
%C A375186 a(n-4) for n>3 is the number of equivalence classes of binary words of length n for the subword 100110 (see A317669 for further explanation).
%C A375186 a(n) is the number of compositions of n+5 into parts 1, 6, 9, 12, 15, 18, ...
%H A375186 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1,0,1).
%F A375186 a(n) = a(n-1) + a(n-3) - a(n-4) + a(n-6) for n>= 6.
%F A375186 G.f.: (1 + x + x^2 + x^4 + x^5)/(1 - x - x^3 + x^4 - x^6).
%e A375186 For n = 6, the 10 subsets are {}, {1}, {2}, {3}, {4}, {1,4}, {5}, {2,5}, {6}, {3,6}.
%t A375186 CoefficientList[Series[(1 + x + x^2 + x^4 + x^5)/(1 - x - x^3 + x^4 - x^6),{x,0,42}],x]
%t A375186 LinearRecurrence[{1, 0, 1, -1, 0, 1}, {1, 2, 3, 4, 6, 8}, 42]
%Y A375186 See A375981 for other sequences related to restricted combinations.
%Y A375186 Column k=27 of A376033.
%K A375186 easy,nonn,changed
%O A375186 0,2
%A A375186 _Michael A. Allen_, Aug 02 2024

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