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%I #8 Sep 04 2022 21:04:51
%S 22,243,22,1324,243,22,5005,1944,243,22,14586,8805,2844,243,22,36247,
%T 28366,15493,4136,243,22,78448,84067,55318,27213,5964,243,22,154689,
%U 202628,195519,108018,47645,8504,243,22,281470,429069,525960,454487
%N T(n,k) = Number of length n+5 0..k arrays with every six consecutive terms having two times the sum of some two elements equal to the sum of the remaining four.
%C Table starts
%C .22.243....1324......5005......14586.......36247........78448........154689
%C .22.243....1944......8805......28366.......84067.......202628........429069
%C .22.243....2844.....15493......55318......195519.......525960.......1201225
%C .22.243....4136.....27213.....108018......454487......1365188.......3374725
%C .22.243....5964.....47645.....211034.....1054347......3535850.......9493535
%C .22.243....8504.....83045.....412334.....2439587......9128450......26718133
%C .22.243...11964....143925.....805518.....5629189.....23480326......75209315
%C .22.243...18884....263405....1574782....13492099.....61940694.....211999693
%C .22.243...29484....480725....3079710....32245925....162995818.....598200699
%C .22.243...45428....874421....6024336....76837553....427723930....1689449813
%C .22.243...68892...1584425...11786986...182515991...1118943674....4775230927
%C .22.243..102564...2858305...23066566...432099083...2917379528...13507360617
%C .22.243..149644...5130445...45148946..1019449179...7579080652...38234913321
%H R. H. Hardin, <a href="/A249085/b249085.txt">Table of n, a(n) for n = 1..566</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1).
%F k=2: a(n) = a(n-1).
%F k=3: [order 25].
%F k=4: [order 40].
%F Empirical for row n:
%F n=1: [linear recurrence of order 10; also a polynomial of degree 5 plus a linear quasipolynomial with period 6].
%e Some solutions for n=4, k=4
%e ..0....3....3....4....1....1....1....3....2....1....3....1....1....4....2....0
%e ..3....3....3....4....3....1....0....4....0....1....3....4....0....4....4....4
%e ..4....3....0....0....0....3....0....0....3....1....2....0....4....4....2....3
%e ..4....2....3....3....2....0....0....0....3....4....1....3....4....2....0....0
%e ..2....4....1....3....2....2....0....2....0....0....4....0....2....1....4....0
%e ..2....0....2....1....1....2....2....3....1....2....2....4....4....0....3....2
%e ..0....0....3....1....4....1....1....0....2....4....0....1....1....1....2....3
%e ..0....3....0....4....0....1....0....1....0....4....3....1....3....4....1....4
%e ..1....0....0....3....0....0....3....0....0....1....2....0....4....4....2....0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Oct 20 2014