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A246737 T(n,k)=Number of length n+4 0..k arrays with no pair in any consecutive five terms totalling exactly k.

%I A246737 #6 Jul 23 2025 11:31:58
%S A246737 2,12,2,124,16,2,424,260,22,2,1566,1096,548,30,2,3876,5430,2884,1156,
%T A246737 40,2,9368,15960,18966,7612,2436,52,2,18768,47432,66378,66294,19992,
%U A246737 5132,68,2,36250,109552,241544,276762,231414,52112,10812,90,2,63100,246890
%N A246737 T(n,k)=Number of length n+4 0..k arrays with no pair in any consecutive five terms totalling exactly k.
%C A246737 Table starts
%C A246737 .2..12....124.....424......1566.......3876........9368........18768
%C A246737 .2..16....260....1096......5430......15960.......47432.......109552
%C A246737 .2..22....548....2884.....18966......66378......241544.......643048
%C A246737 .2..30...1156....7612.....66294.....276762.....1231304......3780600
%C A246737 .2..40...2436...19992....231414....1152576.....6272072.....22219408
%C A246737 .2..52...5132...52112....807630....4791012....31944440....130526848
%C A246737 .2..68..10812..135776...2818830...19906740...162700376....766650656
%C A246737 .2..90..22780..354428...9838974...82727094...828690200...4502888280
%C A246737 .2.120..47996..926912..34342350..343911336..4220813912..26449024896
%C A246737 .2.160.101124.2426008.119869158.1430080296.21498069128.155366381200
%H A246737 R. H. Hardin, <a href="/A246737/b246737.txt">Table of n, a(n) for n = 1..1661</a>
%F A246737 Empirical for column k:
%F A246737 k=1: a(n) = a(n-1)
%F A246737 k=2: a(n) = a(n-1) +a(n-5)
%F A246737 k=3: a(n) = 2*a(n-1) +a(n-4)
%F A246737 k=4: [order 16]
%F A246737 k=5: a(n) = 3*a(n-1) +a(n-2) +a(n-3) +5*a(n-4) +a(n-5) -a(n-6) -a(n-7)
%F A246737 k=6: [order 23]
%F A246737 k=7: a(n) = 4*a(n-1) +4*a(n-2) +4*a(n-3) +18*a(n-4) +12*a(n-5) -4*a(n-7) -a(n-8)
%F A246737 k=8: [order 24]
%F A246737 k=9: a(n) = 6*a(n-1) +4*a(n-2) +6*a(n-3) +38*a(n-4) +18*a(n-5) -6*a(n-7) -a(n-8)
%F A246737 Empirical for row n:
%F A246737 n=1: 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 A246737 n=2: [order 11]
%F A246737 n=3: [order 13]
%F A246737 n=4: [order 15]
%F A246737 n=5: [order 17]
%F A246737 n=6: [order 19]
%F A246737 n=7: [order 21]
%e A246737 Some solutions for n=4 k=4
%e A246737 ..3....4....3....1....1....0....2....1....1....0....2....3....2....4....0....0
%e A246737 ..3....1....2....4....4....1....0....4....1....0....4....4....4....3....2....0
%e A246737 ..3....1....3....1....2....2....1....2....2....1....3....2....1....4....0....0
%e A246737 ..4....1....4....4....1....1....1....1....4....0....3....3....4....4....0....0
%e A246737 ..4....4....4....1....4....0....0....1....4....0....3....4....4....4....1....0
%e A246737 ..4....1....4....1....1....0....0....1....1....2....3....3....1....3....0....2
%e A246737 ..3....2....2....2....4....1....2....0....1....0....4....3....1....3....2....1
%e A246737 ..4....4....1....1....1....1....0....2....2....1....3....4....2....3....0....0
%Y A246737 Column 2 is A174469(n+18)
%K A246737 nonn,tabl
%O A246737 1,1
%A A246737 _R. H. Hardin_, Sep 02 2014