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A242144 T(n,k)=Number of length n+5 0..k arrays with no consecutive six elements summing to more than 3*k.

%I A242144 #6 Jul 23 2025 11:15:29
%S A242144 42,435,74,2338,1113,132,8688,7862,2902,236,25494,36224,27024,7596,
%T A242144 421,63490,126894,154647,93308,19834,747,140148,367358,647404,663395,
%U A242144 321320,51440,1314,282051,924300,2180310,3319500,2837837,1098260,131950,2318
%N A242144 T(n,k)=Number of length n+5 0..k arrays with no consecutive six elements summing to more than 3*k.
%C A242144 Table starts
%C A242144 ...42....435....2338.....8688.....25494......63490......140148......282051
%C A242144 ...74...1113....7862....36224....126894.....367358......924300.....2088459
%C A242144 ..132...2902...27024...154647....647404....2180310.....6256170....15876783
%C A242144 ..236...7596...93308...663395...3319500...13006484....42564898...121330981
%C A242144 ..421..19834..321320..2837837..16970962...77357343...288712815...924335053
%C A242144 ..747..51440.1098260.12043599..86052208..456215409..1941492045..6980495147
%C A242144 .1314.131950.3708268.50455611.430518585.2653766000.12874102578.51971761446
%H A242144 R. H. Hardin, <a href="/A242144/b242144.txt">Table of n, a(n) for n = 1..532</a>
%F A242144 Empirical for column k:
%F A242144 k=1: [linear recurrence of order 20]
%F A242144 Empirical for row n:
%F A242144 n=1: [polynomial of degree 6]
%F A242144 n=2: [polynomial of degree 7]
%F A242144 n=3: [polynomial of degree 8]
%F A242144 n=4: [polynomial of degree 9]
%F A242144 n=5: [polynomial of degree 10]
%F A242144 n=6: [polynomial of degree 11]
%F A242144 n=7: [polynomial of degree 12]
%e A242144 Some solutions for n=3 k=4
%e A242144 ..2....1....0....0....0....2....0....0....0....0....2....0....1....0....1....2
%e A242144 ..1....0....0....3....3....3....3....0....3....2....2....4....3....3....0....1
%e A242144 ..1....1....4....2....1....0....0....4....1....0....1....3....1....2....1....0
%e A242144 ..4....3....0....2....1....1....3....2....0....2....1....0....0....0....0....1
%e A242144 ..1....0....3....2....3....1....1....0....4....0....1....0....1....1....1....1
%e A242144 ..1....0....1....0....0....2....4....1....1....0....4....2....4....3....2....4
%e A242144 ..1....1....0....2....0....4....0....1....1....2....3....1....2....0....1....0
%e A242144 ..1....2....3....3....2....1....1....3....3....1....1....2....0....1....2....3
%Y A242144 Column 1 is A133551(n+5)
%Y A242144 Column 2 is A212227
%Y A242144 Column 3 is A212466
%K A242144 nonn,tabl
%O A242144 1,1
%A A242144 _R. H. Hardin_, May 05 2014