cp's OEIS Frontend

A375185 Number of subsets of {1,2,...,n} such that no two elements differ by 1, 2, 3, or 5.

%I A375185 #19 Mar 19 2025 08:33:11
%S A375185 1,2,3,4,5,7,9,12,16,22,29,39,52,70,93,125,167,224,299,401,536,718,
%T A375185 960,1286,1720,2303,3081,4125,5519,7388,9886,13233,17708,23702,31719,
%U A375185 42454,56815,76042,101767,136204,182284,243965,326505,436984,584831,782716
%N A375185 Number of subsets of {1,2,...,n} such that no two elements differ by 1, 2, 3, or 5.
%C A375185 a(n-4) for n>3 is the number of equivalence classes of binary words of length n for the subword 100010 (see A317669 for further explanation).
%C A375185 a(n) is the number of compositions of n+5 into parts 1, 6, 10, 14, 18, 22, ...
%H A375185 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1,1).
%H A375185 <a href="/index/Su#sublatts">Index entries for subsets of {1,..,n} with disallowed differences</a>
%F A375185 a(n) = a(n-1) + a(n-4) - a(n-5) + a(n-6) for n >= 6.
%F A375185 G.f.: (1 + x + x^2 + x^3 + x^5)/(1 - x - x^4 + x^5 - x^6).
%e A375185 For n = 6, the 9 subsets are {}, {1}, {2}, {3}, {4}, {5}, {1,5}, {6}, {2,6}.
%t A375185 CoefficientList[Series[(1 + x + x^2 + x^3 + x^5)/(1 - x - x^4 + x^5 - x^6),{x,0,45}],x]
%t A375185 LinearRecurrence[{1, 0, 0, 1, -1, 1}, {1, 2, 3, 4, 5, 7}, 45]
%Y A375185 Column k=23 of A376033.
%K A375185 easy,nonn
%O A375185 0,2
%A A375185 _Michael A. Allen_, Aug 02 2024