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A250419 T(n,k)=Number of length n+1 0..k arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

%I A250419 #8 Jul 23 2025 12:23:25
%S A250419 3,5,6,7,17,10,9,36,38,20,11,65,99,125,36,13,106,205,476,335,72,15,
%T A250419 161,370,1351,1693,1061,136,17,232,606,3154,5982,7504,3069,272,19,321,
%U A250419 927,6433,16790,34415,29221,9495,528,21,430,1345,11906,39916,119364,169352
%N A250419 T(n,k)=Number of length n+1 0..k arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.
%C A250419 Table starts
%C A250419 ....3.....5.......7........9........11........13.........15..........17
%C A250419 ....6....17......36.......65.......106.......161........232.........321
%C A250419 ...10....38......99......205.......370.......606........927........1345
%C A250419 ...20...125.....476.....1351......3154......6433......11906.......20461
%C A250419 ...36...335....1693.....5982.....16790.....39916......84094......161350
%C A250419 ...72..1061....7504....34415....119364....341011.....845358.....1878315
%C A250419 ..136..3069...29221...169352....713260...2399000....6847916....17247435
%C A250419 ..272..9495..123242...904695...4620694..18334295...60473968...173147889
%C A250419 ..528.28221..492076..4547008..28033122.130350889..493271080..1595410130
%C A250419 .1056.86149.2021436.23448029.174036890.947356115.4110606460.15000578409
%H A250419 R. H. Hardin, <a href="/A250419/b250419.txt">Table of n, a(n) for n = 1..313</a>
%F A250419 Empirical for column k:
%F A250419 k=1: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3)
%F A250419 k=2: [order 10]
%F A250419 k=3: [order 29]
%F A250419 Empirical for row n:
%F A250419 n=1: a(n) = 2*n + 1
%F A250419 n=2: a(n) = (1/3)*n^3 + 2*n^2 + (8/3)*n + 1
%F A250419 n=3: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5); also a cubic polynomial plus a constant quasipolynomial with period 2
%F A250419 n=4: [linear recurrence of order 10; also a quintic polynomial plus a linear quasipolynomial with period 3]
%F A250419 n=5: [order 17; also a quintic polynomial plus a quadratic quasipolynomial with period 12]
%e A250419 Some solutions for n=5 k=4
%e A250419 ..3....0....3....1....3....3....2....1....2....0....0....1....2....4....0....3
%e A250419 ..1....2....1....0....4....2....0....3....1....0....0....0....4....0....2....0
%e A250419 ..4....0....0....0....1....4....3....2....2....0....1....0....3....2....2....0
%e A250419 ..3....2....2....2....4....2....0....0....1....2....1....4....2....1....4....2
%e A250419 ..2....3....3....0....4....4....4....3....2....1....4....1....3....4....1....1
%e A250419 ..1....2....1....1....3....4....0....3....3....1....0....3....3....0....2....1
%Y A250419 Column 1 is A005418(n+2)
%Y A250419 Row 1 is A004273(n+1)
%Y A250419 Row 2 is A084990(n+1)
%K A250419 nonn,tabl
%O A250419 1,1
%A A250419 _R. H. Hardin_, Nov 22 2014