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A180283
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Number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to 3.
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1
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3, 12, 50, 195, 735, 2716, 9912, 35850, 128865, 461175, 1645215, 5855941, 20810153, 73870748, 262029364, 929031504, 3293120337, 11672207262, 41373395052, 146674116501, 520093043437, 1844704839175, 6544970763175, 23229252652125
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OFFSET
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3,1
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LINKS
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MAPLE
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f:= proc(m, n) option remember;
if m > 3*n or m < 3 then return 0 fi;
g(m-3, n-1) + add(procname(m-i, n-1), i=0..2)
end proc:
g:= proc(m, n) option remember;
if m > 3*n then return 0 fi;
add(procname(m-i, n-1), i=0..min(m, 3))
end proc:
g(0, 0):= 1:
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MATHEMATICA
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b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i == 0, 0, Sum[b[n-j, i-1, k], {j, 0, Min[n, k]}]]];
a[n_] := b[n, n, 3] - b[n, n, 2];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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