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A250646 T(n,k)=Number of length n+1 0..k arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

%I A250646 #8 Jul 23 2025 12:38:52
%S A250646 1,1,6,1,17,6,1,36,23,20,1,65,44,125,28,1,106,89,476,280,72,1,161,134,
%T A250646 1293,1424,1061,120,1,232,219,2954,4853,7696,2870,272,1,321,296,5901,
%U A250646 12473,34441,28238,9495,496,1,430,433,10766,28379,120114,163043,126482
%N A250646 T(n,k)=Number of length n+1 0..k arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.
%C A250646 Table starts
%C A250646 ......1.........1............1.............1...............1...............1
%C A250646 ......6........17...........36............65.............106.............161
%C A250646 ......6........23...........44............89.............134.............219
%C A250646 .....20.......125..........476..........1293............2954............5901
%C A250646 .....28.......280.........1424..........4853...........12473...........28379
%C A250646 .....72......1061.........7696.........34441..........120114..........332827
%C A250646 ....120......2870........28238........163043..........677505.........2225195
%C A250646 ....272......9495.......126482........915663.........4749950........18399217
%C A250646 ....496.....27507.......491943.......4537317........28200435.......129137886
%C A250646 ...1056.....86149......2059700......23671551.......177863786.......953809557
%C A250646 ...2016....255704......8161068.....118358549......1063874048......6704767056
%C A250646 ...4160....782393.....33268124.....601565301......6491819162.....47777146765
%C A250646 ...8128...2341381....132637221....3011330309.....38892883673....335147823244
%C A250646 ..16512...7090347....534771362...15155615651....234724691398...2360792885729
%C A250646 ..32640..21271463...2136620867...75845220727...1407192408230..16540740396740
%C A250646 ..65792..64109181...8574987528..380253505733...8460554956974.116054610957529
%C A250646 .130816.192439733..34285733053.1902264449049..50741165814612.812699929957712
%C A250646 .262656.578665211.137334914170.9522274036139.304671802762820
%H A250646 R. H. Hardin, <a href="/A250646/b250646.txt">Table of n, a(n) for n = 1..267</a>
%F A250646 Empirical for column k:
%F A250646 k=1: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3)
%F A250646 k=2: [order 10]
%F A250646 k=3: [order 24] for n>25
%F A250646 Empirical for row n:
%F A250646 n=1: a(n) = a(n-1)
%F A250646 n=2: a(n) = (1/3)*n^3 + 2*n^2 + (8/3)*n + 1
%F A250646 n=3: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +3*a(n-5) +a(n-6) -a(n-7); also a polynomial of degree 3 plus a quasipolynomial of degree 2 with period 2
%F A250646 n=4: [order 14; also a polynomial of degree 5 plus a quasipolynomial of degree 2 with period 6]
%F A250646 n=5: [order 25; also a polynomial of degree 5 plus a quasipolynomial of degree 4 with period 12]
%e A250646 Some solutions for n=5 k=4
%e A250646 ..4....2....1....4....0....1....1....2....0....2....1....2....2....4....4....3
%e A250646 ..1....1....1....1....2....2....0....2....0....1....0....1....2....0....1....3
%e A250646 ..1....0....1....1....2....0....0....1....1....0....2....0....2....2....0....1
%e A250646 ..0....1....0....0....0....0....1....1....2....4....3....4....1....3....2....2
%e A250646 ..1....1....1....3....1....4....3....0....1....3....3....3....1....0....1....4
%e A250646 ..3....0....4....3....3....3....3....0....0....2....0....3....3....2....0....4
%Y A250646 Column 1 is A113979(n+2)
%Y A250646 Row 2 is A084990(n+1)
%K A250646 nonn,tabl
%O A250646 1,3
%A A250646 _R. H. Hardin_, Nov 26 2014