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%I #5 Mar 31 2012 12:36:19
%S 2,12,18,39,33,72,43,105,69,123,72,190,83,169,151,217,108,276,120,297,
%T 206,261,150,427,179,318,259,405,185,509,201,452,326,413,277,652,228,
%U 470,383,626,263,688,276,631,501,559,303,893,323,673,509,748,341,883,418,831
%N Number of nondecreasing arrangements of 7 numbers in 0..n with the last equal to n and each after the second equal to the sum of one or two of the preceding three
%C Row 5 of A190041
%H R. H. Hardin, <a href="/A190044/b190044.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = -4*a(n-1) -13*a(n-2) -33*a(n-3) -75*a(n-4) -152*a(n-5) -286*a(n-6) -500*a(n-7) -826*a(n-8) -1292*a(n-9) -1929*a(n-10) -2753*a(n-11) -3772*a(n-12) -4965*a(n-13) -6291*a(n-14) -7671*a(n-15) -9002*a(n-16) -10148*a(n-17) -10961*a(n-18) -11284*a(n-19) -10976*a(n-20) -9925*a(n-21) -8069*a(n-22) -5411*a(n-23) -2025*a(n-24) +1935*a(n-25) +6252*a(n-26) +10648*a(n-27) +14823*a(n-28) +18464*a(n-29) +21297*a(n-30) +23091*a(n-31) +23708*a(n-32) +23091*a(n-33) +21297*a(n-34) +18464*a(n-35) +14823*a(n-36) +10648*a(n-37) +6252*a(n-38) +1935*a(n-39) -2025*a(n-40) -5411*a(n-41) -8069*a(n-42) -9925*a(n-43) -10976*a(n-44) -11284*a(n-45) -10961*a(n-46) -10148*a(n-47) -9002*a(n-48) -7671*a(n-49) -6291*a(n-50) -4965*a(n-51) -3772*a(n-52) -2753*a(n-53) -1929*a(n-54) -1292*a(n-55) -826*a(n-56) -500*a(n-57) -286*a(n-58) -152*a(n-59) -75*a(n-60) -33*a(n-61) -13*a(n-62) -4*a(n-63) -a(n-64)
%e Some solutions for n=3
%e ..0....0....2....1....1....1....1....1....0....0....0....0....1....3....1....1
%e ..1....3....3....1....1....2....1....1....1....1....1....1....1....3....1....1
%e ..1....3....3....1....1....2....2....1....1....1....1....1....2....3....1....1
%e ..1....3....3....1....2....3....2....1....2....2....1....1....3....3....2....1
%e ..2....3....3....1....3....3....3....2....2....3....1....2....3....3....2....2
%e ..3....3....3....2....3....3....3....3....3....3....2....2....3....3....3....2
%e ..3....3....3....3....3....3....3....3....3....3....3....3....3....3....3....3
%K nonn
%O 1,1
%A _R. H. Hardin_ May 04 2011
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