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A213213 Number of distinct products i*j*k over all triples (i,j,k) with i,j,k>=0 and i+j+k <= n. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

This sequence is in reply to an extension request made in A100450.

LINKS

Robert Price and Alois P. Heinz, Table of n, a(n) for n = 0..1000 (terms n = 0..200 from Robert Price)

FORMULA

a(n) = (A213207(n)+1)/2.

MAPLE

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:

seq(a(n), n=0..60);  # Alois P. Heinz, Mar 02 2013

MATHEMATICA

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}]

CROSSREFS

Cf. A018805, A027430, A100448, A100449, A100450, A213207, A213208, A213212.

Sequence in context: A177332 A318155 A282569 * A319470 A115001 A338380

Adjacent sequences:  A213210 A213211 A213212 * A213214 A213215 A213216

KEYWORD

nonn,easy

AUTHOR

Robert Price, Mar 02 2013

STATUS

approved

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Last modified June 17 05:03 EDT 2021. Contains 345080 sequences. (Running on oeis4.)