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A200251 T(n,k)=Number of 0..k arrays x(0..n-1) of n elements with each no smaller than the sum of its previous elements modulo (k+1).

%I A200251 #7 Jun 02 2025 07:17:52
%S A200251 2,3,3,4,6,5,5,10,12,8,6,15,26,24,13,7,21,45,69,48,21,8,28,75,135,181,
%T A200251 96,34,9,36,112,267,405,476,192,55,10,45,164,448,951,1215,1252,384,89,
%U A200251 11,55,225,750,1792,3387,3645,3292,768,144,12,66,305,1125,3434,7168,12063
%N A200251 T(n,k)=Number of 0..k arrays x(0..n-1) of n elements with each no smaller than the sum of its previous elements modulo (k+1).
%C A200251 Table starts
%C A200251 ...2....3.....4.....5......6.......7.......8........9.......10........11
%C A200251 ...3....6....10....15.....21......28......36.......45.......55........66
%C A200251 ...5...12....26....45.....75.....112.....164......225......305.......396
%C A200251 ...8...24....69...135....267.....448.....750.....1125.....1690......2376
%C A200251 ..13...48...181...405....951....1792....3434.....5625.....9365.....14256
%C A200251 ..21...96...476..1215...3387....7168...15724....28125....51895.....85536
%C A200251 ..34..192..1252..3645..12063...28672...71970...140625...287570....513216
%C A200251 ..55..384..3292.10935..42963..114688..329455...703125..1593535...3079296
%C A200251 ..89..768..8657.32805.153015..458752.1508139..3515625..8830385..18475776
%C A200251 .144.1536.22765.98415.544971.1835008.6903702.17578125.48932530.110854656
%H A200251 R. H. Hardin, <a href="/A200251/b200251.txt">Table of n, a(n) for n = 1..9999</a>
%F A200251 Empirical: T(n,2k) = (2*k+1)*(k+1)^(n-1)
%e A200251 Some solutions for n=7 k=6
%e A200251 ..1....2....4....0....1....0....4....0....1....4....2....3....1....3....3....3
%e A200251 ..3....5....6....3....2....6....5....4....1....5....5....4....2....5....3....4
%e A200251 ..4....5....5....6....5....6....5....6....6....2....1....0....5....6....6....1
%e A200251 ..6....5....3....2....6....5....3....6....2....5....3....0....3....0....6....1
%e A200251 ..2....5....6....6....0....6....4....3....5....2....5....5....4....2....5....5
%e A200251 ..6....2....5....6....2....2....2....5....2....4....5....5....4....5....6....2
%e A200251 ..5....4....1....3....4....4....2....5....3....3....1....3....6....1....6....5
%Y A200251 Column 1 is A000045(n+2)
%Y A200251 Column 2 is A003945
%Y A200251 Column 3 is A099234(n+1)
%Y A200251 Column 4 is A005030(n-1)
%Y A200251 Column 6 is A002042(n-1)
%Y A200251 Row 2 is A000217(n+1)
%K A200251 nonn,tabl
%O A200251 1,1
%A A200251 _R. H. Hardin_ Nov 15 2011