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A241936 T(n,k)=Number of length n+4 0..k arrays with no consecutive five elements summing to more than 2*k.

%I A241936 #7 Jul 23 2025 11:14:52
%S A241936 16,96,26,357,218,43,1007,1043,509,71,2373,3599,3150,1187,116,4928,
%T A241936 10031,13339,9500,2727,186,9318,24052,44063,49355,28153,6105,300,
%U A241936 16389,51570,122162,193179,179145,80983,13783,487,27214,101421,297324,619132,829867
%N A241936 T(n,k)=Number of length n+4 0..k arrays with no consecutive five elements summing to more than 2*k.
%C A241936 Table starts
%C A241936 ..16....96....357....1007.....2373.....4928......9318.....16389......27214
%C A241936 ..26...218...1043....3599....10031....24052.....51570....101421.....186208
%C A241936 ..43...509...3150...13339....44063...122162....297324....654345....1329163
%C A241936 ..71..1187...9500...49355...193179...619132...1710198...4211175....9462805
%C A241936 .116..2727..28153..179145...829867..3072022...9624440..26502761...65852820
%C A241936 .186..6105..80983..629639..3446359.14718452..52254450.160807307..441594824
%C A241936 .300.13783.235307.2237881.14484953.71410234.287426800.988849923.3001975962
%H A241936 R. H. Hardin, <a href="/A241936/b241936.txt">Table of n, a(n) for n = 1..2353</a>
%F A241936 Empirical for column k:
%F A241936 k=1: a(n)=a(n-1)+a(n-3)+2*a(n-5)-a(n-8)-a(n-10)
%F A241936 k=2: [order 45]
%F A241936 Empirical for row n:
%F A241936 n=1: [polynomial of degree 5]
%F A241936 n=2: [polynomial of degree 6]
%F A241936 n=3: [polynomial of degree 7]
%F A241936 n=4: [polynomial of degree 8]
%F A241936 n=5: [polynomial of degree 9]
%F A241936 n=6: [polynomial of degree 10]
%F A241936 n=7: [polynomial of degree 11]
%e A241936 Some solutions for n=4 k=4
%e A241936 ..4....2....0....2....1....1....3....0....1....3....1....1....1....3....4....0
%e A241936 ..1....1....1....0....1....4....0....1....2....0....2....0....1....1....0....0
%e A241936 ..3....1....1....4....2....1....0....1....1....4....2....0....0....0....0....2
%e A241936 ..0....2....0....2....2....2....1....0....0....0....0....0....3....1....0....0
%e A241936 ..0....2....1....0....2....0....1....1....2....1....2....0....0....1....0....0
%e A241936 ..0....1....1....1....1....1....0....4....2....1....0....2....0....3....0....0
%e A241936 ..4....0....2....0....0....1....1....0....0....1....3....3....3....0....0....4
%e A241936 ..0....0....0....2....0....0....1....3....1....0....1....3....1....1....1....4
%Y A241936 Column 1 is A120118(n+4)
%K A241936 nonn,tabl
%O A241936 1,1
%A A241936 _R. H. Hardin_, May 02 2014