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A245950 T(n,k)=Number of length n+3 0..k arrays with some pair in every consecutive four terms totalling exactly k.

%I A245950 #6 Jul 23 2025 11:30:22
%S A245950 14,71,26,196,197,48,453,676,545,88,834,1889,2304,1501,162,1435,3966,
%T A245950 7769,7744,4145,298,2216,7669,18384,31465,26244,11441,548,3305,13064,
%U A245950 39721,82968,128649,88804,31577,1008,4630,21281,73728,199141,381222
%N A245950 T(n,k)=Number of length n+3 0..k arrays with some pair in every consecutive four terms totalling exactly k.
%C A245950 Table starts
%C A245950 ...14.....71......196.......453.......834.......1435........2216........3305
%C A245950 ...26....197......676......1889......3966.......7669.......13064.......21281
%C A245950 ...48....545.....2304......7769.....18384......39721.......73728......130193
%C A245950 ...88...1501.....7744.....31465.....82968.....199141......397504......754321
%C A245950 ..162...4145....26244....128649....381222....1021225.....2217096.....4555697
%C A245950 ..298..11441....88804....525041...1744494....5208673....12257032....27206945
%C A245950 ..548..31577...300304...2141609...7972932...26526337....67596992...161991665
%C A245950 .1008..87161..1016064...8740385..36489120..135336793...373997376...968575361
%C A245950 .1854.240581..3437316..35666177.166920402..690045061..2066660136..5781493025
%C A245950 .3410.664051.11628100.145538749.763564758.3518298991.11420014856.34510470937
%H A245950 R. H. Hardin, <a href="/A245950/b245950.txt">Table of n, a(n) for n = 1..9999</a>
%F A245950 Empirical for column k:
%F A245950 k=1: a(n) = a(n-1) +a(n-2) +a(n-3)
%F A245950 k=2: a(n) = 2*a(n-1) +2*a(n-2) +a(n-3) -a(n-4) -2*a(n-5) -2*a(n-6) -a(n-7) +a(n-8) +a(n-9)
%F A245950 k=3: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) -a(n-4) -a(n-6)
%F A245950 k=4: [order 15]
%F A245950 k=5: a(n) = 3*a(n-1) +5*a(n-2) +13*a(n-3) -13*a(n-4) -a(n-5) -3*a(n-6) +a(n-7)
%F A245950 k=6: [order 16]
%F A245950 k=7: a(n) = 3*a(n-1) +9*a(n-2) +31*a(n-3) -19*a(n-4) -3*a(n-5) -5*a(n-6) +a(n-7)
%F A245950 k=8: [order 16]
%F A245950 k=9: a(n) = 3*a(n-1) +13*a(n-2) +57*a(n-3) -25*a(n-4) -5*a(n-5) -7*a(n-6) +a(n-7)
%F A245950 Empirical for row n:
%F A245950 n=1: a(n) = 2*a(n-1) +a(n-2) -4*a(n-3) +a(n-4) +2*a(n-5) -a(n-6)
%F A245950 n=2: a(n) = 2*a(n-1) +2*a(n-2) -6*a(n-3) +6*a(n-5) -2*a(n-6) -2*a(n-7) +a(n-8)
%F A245950 n=3: a(n) = 3*a(n-1) -8*a(n-3) +6*a(n-4) +6*a(n-5) -8*a(n-6) +3*a(n-8) -a(n-9)
%F A245950 n=4: [order 10]
%F A245950 n=5: [order 12]
%F A245950 n=6: [order 13]
%F A245950 n=7: [order 14]
%e A245950 Some solutions for n=4 k=4
%e A245950 ..1....4....0....2....1....3....3....0....3....2....0....4....0....3....2....2
%e A245950 ..3....2....1....1....4....2....1....4....0....4....1....0....4....4....0....2
%e A245950 ..3....2....4....3....0....2....1....1....4....1....4....3....4....2....2....2
%e A245950 ..2....1....2....0....0....0....4....0....3....3....3....1....3....1....2....0
%e A245950 ..1....3....0....1....3....4....3....2....2....2....0....1....0....0....2....4
%e A245950 ..3....4....3....0....1....2....1....3....0....1....1....4....2....3....1....1
%e A245950 ..1....2....1....4....0....3....1....2....1....4....1....0....1....1....1....4
%Y A245950 Column 1 is A135491(n+3)
%Y A245950 Column 3 is A203536(n+5)
%K A245950 nonn,tabl
%O A245950 1,1
%A A245950 _R. H. Hardin_, Aug 08 2014