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A200668 T(n,k)=Number of 0..k arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo (k+1).

%I A200668 #7 Jun 02 2025 07:19:35
%S A200668 2,3,3,4,6,5,5,10,12,8,6,15,26,24,12,7,21,45,69,46,17,8,28,75,135,175,
%T A200668 89,25,9,36,112,267,406,432,176,36,10,45,164,448,938,1217,1076,350,51,
%U A200668 11,55,225,750,1813,3283,3650,2671,697,72,12,66,305,1125,3414,7322,11516,10959
%N A200668 T(n,k)=Number of 0..k arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo (k+1).
%C A200668 Table starts
%C A200668 ..2....3.....4.....5......6.......7.......8........9.......10........11
%C A200668 ..3....6....10....15.....21......28......36.......45.......55........66
%C A200668 ..5...12....26....45.....75.....112.....164......225......305.......396
%C A200668 ..8...24....69...135....267.....448.....750.....1125.....1690......2376
%C A200668 .12...46...175...406....938....1813....3414.....5682.....9412.....14443
%C A200668 .17...89...432..1217...3283....7322...15504....28743....52389.....87890
%C A200668 .25..176..1076..3650..11516...29536...70412...145431...291683....534853
%C A200668 .36..350..2671.10959..40399..119066..319532...735519..1623152...3252623
%C A200668 .51..697..6627.32941.141745..479993.1449895..3719534..9031554..19778869
%C A200668 .72.1391.16421.99044.497298.1935168.6578528.18809812.50252326.120270942
%H A200668 R. H. Hardin, <a href="/A200668/b200668.txt">Table of n, a(n) for n = 1..1497</a>
%e A200668 Some solutions for n=7 k=6
%e A200668 ..4....0....4....6....2....3....4....2....5....1....0....1....1....5....3....1
%e A200668 ..5....0....5....6....6....6....6....5....6....2....4....2....4....5....5....4
%e A200668 ..5....1....5....6....6....5....6....0....6....3....6....4....6....3....2....6
%e A200668 ..6....1....4....4....2....6....6....0....4....6....4....1....5....6....4....6
%e A200668 ..3....2....5....4....2....3....5....6....5....5....5....2....4....1....4....4
%e A200668 ..2....4....5....6....6....4....3....6....5....5....4....0....2....4....5....4
%e A200668 ..4....2....5....5....5....6....0....5....3....4....6....5....5....6....6....5
%Y A200668 Row 2 is A000217(n+1)
%Y A200668 Row 3 is A200252
%Y A200668 Row 4 is A200253
%K A200668 nonn,tabl
%O A200668 1,1
%A A200668 _R. H. Hardin_ Nov 20 2011