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A213213
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Number of distinct products i*j*k over all triples (i,j,k) with i,j,k>=0 and i+j+k <= n.
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7
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1, 1, 1, 2, 3, 5, 7, 10, 13, 18, 22, 28, 33, 40, 46, 56, 64, 75, 84, 97, 109, 125, 137, 156, 170, 192, 210, 232, 251, 276, 296, 322, 347, 376, 400, 435, 463, 498, 529, 567, 600, 641, 674, 720, 758, 808, 849, 901, 942, 1001, 1051, 1110, 1157, 1225, 1275
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OFFSET
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0,4
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COMMENTS
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This sequence is in reply to an extension request made in A100450.
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LINKS
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FORMULA
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MAPLE
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h:= proc() true end:
b:= proc(n) local c, i, j, p;
c:=0;
for i to iquo(n, 3) do
for j from i to iquo(n-i, 2) do p:= i*j*(n-i-j);
if h(p) then h(p):= false; c:=c+1 fi
od
od; c
end:
a:= proc(n) a(n):= `if`(n=0, 1, a(n-1) +b(n)) end:
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MATHEMATICA
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f[n_] := Length[ Union[ Flatten[ Table[ If[ i+j+k <= n, i*j*k, 0], {i, 0, n}, {j, 0, n}, {k, 0, n}], 2]]]; Table[ f[n], {n, 0, 200}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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