cp's OEIS Frontend

A213458 Number of 0..3 arrays of length n+3 with sum less than 6 in any length 4 subsequence (=less than 50% duty cycle).

%I A213458 #9 Jun 02 2025 08:01:07
%S A213458 106,310,927,2735,7803,22506,65425,190318,551598,1597812,4632940,
%T A213458 13439852,38977905,113018097,327714656,950345164,2755932228,
%U A213458 7991769082,23174685375,67202984107,194879111652,565120621828,1638762823886
%N A213458 Number of 0..3 arrays of length n+3 with sum less than 6 in any length 4 subsequence (=less than 50% duty cycle).
%C A213458 Column 2 of A213464
%H A213458 R. H. Hardin, <a href="/A213458/b213458.txt">Table of n, a(n) for n = 1..210</a>
%F A213458 Empirical: a(n) = 2*a(n-1) +a(n-2) +a(n-3) +16*a(n-4) -8*a(n-5) -13*a(n-6) -8*a(n-7) -64*a(n-8) +15*a(n-9) +37*a(n-10) +25*a(n-11) +136*a(n-12) -54*a(n-13) -36*a(n-14) -34*a(n-15) -173*a(n-16) +107*a(n-17) +19*a(n-18) +14*a(n-19) +144*a(n-20) -129*a(n-21) +4*a(n-22) +12*a(n-23) -103*a(n-24) +98*a(n-25) -18*a(n-26) -15*a(n-27) +75*a(n-28) -39*a(n-29) +18*a(n-30) +6*a(n-31) -40*a(n-32) +9*a(n-33) -8*a(n-34) -a(n-35) +11*a(n-36) -a(n-37) +a(n-38) -a(n-40)
%e A213458 Some solutions for n=3
%e A213458 ..0....2....0....1....2....1....0....1....2....1....3....1....1....0....1....0
%e A213458 ..0....0....3....0....1....2....0....0....1....2....0....0....1....0....0....0
%e A213458 ..0....3....1....0....0....1....0....0....2....2....2....1....1....0....0....1
%e A213458 ..0....0....1....0....1....0....2....1....0....0....0....2....1....1....1....0
%e A213458 ..1....0....0....0....1....0....0....1....1....1....0....0....2....0....2....1
%e A213458 ..3....2....0....3....0....3....0....0....2....2....0....0....1....2....0....0
%K A213458 nonn
%O A213458 1,1
%A A213458 _R. H. Hardin_ Jun 12 2012