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A215190 T(n,k)=Number of arrays of n 0..k integers with no sum of consecutive elements equal to a disjoint adjacent sum of an equal number of elements.

%I A215190 #7 Jul 22 2025 23:23:05
%S A215190 2,3,2,4,6,2,5,12,12,0,6,20,36,18,0,7,30,80,88,30,0,8,42,150,276,216,
%T A215190 30,0,9,56,252,664,954,440,18,0,10,72,392,1366,2940,2898,896,0,0,11,
%U A215190 90,576,2512,7404,11756,8808,1626,0,0,12,110,810,4264,16092,36864,46972,24014
%N A215190 T(n,k)=Number of arrays of n 0..k integers with no sum of consecutive elements equal to a disjoint adjacent sum of an equal number of elements.
%C A215190 Table starts
%C A215190 .2..3....4......5.......6........7.........8..........9.........10........11
%C A215190 .2..6...12.....20......30.......42........56.........72.........90.......110
%C A215190 .2.12...36.....80.....150......252.......392........576........810......1100
%C A215190 .0.18...88....276.....664.....1366......2512.......4264.......6800.....10330
%C A215190 .0.30..216....954....2940.....7404.....16092......31560......57072.....96990
%C A215190 .0.30..440...2898...11756....36864.....95832.....219092.....452368....864810
%C A215190 .0.18..896...8808...46972...183438....570460....1520506....3584736...7709744
%C A215190 .0..0.1626..24014..172046...848802...3191034....9990182...27052236..65759590
%C A215190 .0..0.2980..65462..630456..3931086..17862744...65678336..204247760.561117076
%C A215190 .0..0.4692.160670.2139436.17086156..94691966..411561564.1477403080
%C A215190 .0..0.7214.394750.7274062.74389138.502572562.2581475090
%C A215190 Column 1 is zero for n>=4
%C A215190 Column 2 is zero for n>=8
%C A215190 Column 3 is zero for n>=51
%H A215190 R. H. Hardin, <a href="/A215190/b215190.txt">Table of n, a(n) for n = 1..164</a>
%e A215190 Some solutions for n=6 k=4
%e A215190 ..1....4....0....0....0....0....4....3....0....3....1....4....3....3....1....2
%e A215190 ..3....3....3....3....4....4....2....4....3....0....3....2....0....4....0....3
%e A215190 ..2....2....4....0....0....3....0....0....1....4....1....4....2....2....3....0
%e A215190 ..0....1....3....4....2....2....4....2....4....3....2....3....4....0....4....4
%e A215190 ..4....2....0....2....0....4....3....3....3....0....1....4....0....3....1....0
%e A215190 ..3....0....1....3....4....2....4....4....1....2....4....1....3....2....4....3
%Y A215190 Row 2 is A002378
%Y A215190 Row 3 is A011379
%K A215190 nonn,tabl
%O A215190 1,1
%A A215190 _R. H. Hardin_ Aug 05 2012