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A241964 T(n,k)=Number of length n+3 0..k arrays with no consecutive four elements summing to more than 2*k.

%I A241964 #6 Jul 23 2025 11:15:06
%S A241964 11,50,19,150,124,33,355,486,311,57,721,1421,1597,775,97,1316,3437,
%T A241964 5778,5211,1895,166,2220,7280,16660,23320,16649,4663,285,3525,13980,
%U A241964 40978,80132,92037,53553,11518,489,5335,24897,89622,228826,376559,365810
%N A241964 T(n,k)=Number of length n+3 0..k arrays with no consecutive four elements summing to more than 2*k.
%C A241964 Table starts
%C A241964 ..11....50....150.....355.....721.....1316......2220......3525.......5335
%C A241964 ..19...124....486....1421....3437.....7280.....13980.....24897......41767
%C A241964 ..33...311...1597....5778...16660....40978.....89622....179079.....333091
%C A241964 ..57...775...5211...23320...80132...228826....569874...1277427....2634115
%C A241964 ..97..1895..16649...92037..376559..1247602...3536286...8889273...20314789
%C A241964 .166..4663..53553..365810.1782453..6853011..22111157..62336336..157897575
%C A241964 .285.11518.172980.1460409.8476317.37822419.138925925.439298830.1233421948
%H A241964 R. H. Hardin, <a href="/A241964/b241964.txt">Table of n, a(n) for n = 1..9999</a>
%F A241964 Empirical for column k:
%F A241964 k=1: a(n) = a(n-1) +a(n-2) +a(n-4) -a(n-6)
%F A241964 k=2: [order 17]
%F A241964 k=3: [order 44]
%F A241964 k=4: [order 85]
%F A241964 Empirical for row n:
%F A241964 n=1: a(n) = (1/2)*n^4 + (7/3)*n^3 + 4*n^2 + (19/6)*n + 1
%F A241964 n=2: a(n) = (23/60)*n^5 + (9/4)*n^4 + (21/4)*n^3 + (25/4)*n^2 + (58/15)*n + 1
%F A241964 n=3: [polynomial of degree 6]
%F A241964 n=4: [polynomial of degree 7]
%F A241964 n=5: [polynomial of degree 8]
%F A241964 n=6: [polynomial of degree 9]
%F A241964 n=7: [polynomial of degree 10]
%e A241964 Some solutions for n=4 k=4
%e A241964 ..0....2....0....4....4....4....3....0....4....2....2....3....2....0....3....0
%e A241964 ..3....2....4....2....3....0....3....0....1....3....2....1....4....2....4....0
%e A241964 ..2....1....1....0....0....0....0....3....0....0....1....0....0....1....0....2
%e A241964 ..0....3....0....1....0....2....2....1....2....1....2....0....2....3....0....1
%e A241964 ..0....0....0....2....0....3....0....1....2....0....2....1....0....1....0....2
%e A241964 ..1....0....0....1....0....0....3....1....4....1....2....3....3....1....2....0
%e A241964 ..3....3....0....4....3....2....3....4....0....0....2....0....3....1....3....3
%Y A241964 Column 1 is A118647(n+3)
%Y A241964 Column 2 is A212226
%Y A241964 Column 3 is A212465
%Y A241964 Row 1 is A212560(n+1)
%K A241964 nonn,tabl
%O A241964 1,1
%A A241964 _R. H. Hardin_, May 03 2014