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A207100 T(n,k)=Number of 0..k arrays x(0..n-1) of n elements with each no smaller than the sum of its two previous neighbors modulo (k+1).

%I A207100 #7 Jun 02 2025 07:40:40
%S A207100 2,3,3,4,6,5,5,10,12,8,6,15,26,26,12,7,21,45,68,55,18,8,28,75,140,176,
%T A207100 115,27,9,36,112,274,441,458,239,40,10,45,164,462,989,1382,1193,498,
%U A207100 59,11,55,225,760,1904,3579,4322,3103,1038,87,12,66,305,1158,3504,7868
%N A207100 T(n,k)=Number of 0..k arrays x(0..n-1) of n elements with each no smaller than the sum of its two previous neighbors modulo (k+1).
%C A207100 Table starts
%C A207100 ..2....3.....4......5......6.......7.......8........9.......10........11
%C A207100 ..3....6....10.....15.....21......28......36.......45.......55........66
%C A207100 ..5...12....26.....45.....75.....112.....164......225......305.......396
%C A207100 ..8...26....68....140....274.....462.....760.....1158.....1720......2431
%C A207100 .12...55...176....441....989....1904....3504.....5925.....9652.....14850
%C A207100 .18..115...458...1382...3579....7868...16224....30390....54294.....90959
%C A207100 .27..239..1193...4322..12964...32531...75114...155922...305362....557095
%C A207100 .40..498..3103..13511..46952..134517..347794...800088..1717686...3412442
%C A207100 .59.1038..8069..42238.170076..556259.1610482..4105829..9663330..20904257
%C A207100 .87.2162.20982.132051.616065.2300219.7457403.21069969.54364034.128056753
%H A207100 R. H. Hardin, <a href="/A207100/b207100.txt">Table of n, a(n) for n = 1..9999</a>
%e A207100 Some solutions for n=5 k=3
%e A207100 ..2....2....0....0....0....1....0....3....2....2....3....1....0....0....2....0
%e A207100 ..2....2....1....0....0....1....3....3....3....2....3....3....0....3....3....1
%e A207100 ..1....2....3....0....3....3....3....3....1....2....2....1....2....3....2....3
%e A207100 ..3....3....3....2....3....2....2....2....3....0....3....3....3....2....3....0
%e A207100 ..1....1....3....2....3....1....3....3....2....3....3....3....3....2....2....3
%Y A207100 Column 1 is A020745(n-2)
%Y A207100 Row 2 is A000217(n+1)
%Y A207100 Row 3 is A199771(n+1)
%K A207100 nonn,tabl
%O A207100 1,1
%A A207100 _R. H. Hardin_ Feb 15 2012