A374711 -id:A374711 - cp's OEIS frontend

A374707 Number of distinct sums i^3 + j^3 for 0<=i<=j<=n.

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 90, 104, 119, 135, 151, 169, 188, 208, 229, 251, 274, 298, 322, 348, 375, 402, 431, 461, 492, 524, 556, 590, 623, 659, 695, 733, 772, 811, 851, 893, 936, 980, 1025, 1071, 1118, 1166, 1213, 1263, 1314, 1365, 1418, 1471, 1525, 1580, 1637, 1695, 1753

Offset: 0

Seiichi Manyama, Jul 17 2024

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A374710, A374711.

Cf. A047800, A061791.

a(n) = my(v=vector(2*n^3+1)); for(i=0, n, for(j=i, n, v[i^3+j^3+1]+=1)); sum(i=1, #v, v[i]>0);

A374714 Number of distinct sums i^3 + j^3 + k^3 + l^3 for 1<=i<=j<=k<=l<=n.

Original entry on oeis.org

1, 5, 15, 35, 70, 119, 202, 317, 473, 671, 902, 1138, 1515, 2008, 2521, 3039, 3758, 4592, 5539, 6657, 7879, 9209, 10797, 12304, 14243, 16371, 18348, 21006, 23816, 26563, 29848, 33046, 36698, 40190, 44885, 49068, 54040, 59479, 64762, 70420, 76810, 83414, 90659, 98158, 105838, 114127, 123048

Offset: 1

Seiichi Manyama, Jul 17 2024

nonn

Cf. A061791, A374713.

Cf. A374711, A374716.

a(n) = my(v=vector(4*n^3)); for(i=1, n, for(j=i, n, for(k=j, n, for(l=k, n, v[i^3+j^3+k^3+l^3]+=1)))); sum(i=1, #v, v[i]>0);

def A374714(n): return len({i**3+j**3+k**3+l**3 for i in range(1,n+1) for j in range(i,n+1) for k in range(j,n+1) for l in range(k,n+1)}) # Chai Wah Wu, Jul 18 2024

A374710 Number of distinct sums i^3 + j^3 + k^3 for 0<=i<=j<=k<=n.

Original entry on oeis.org

1, 4, 10, 20, 35, 56, 82, 117, 162, 215, 279, 352, 426, 528, 645, 772, 899, 1057, 1235, 1429, 1647, 1883, 2133, 2415, 2694, 3022, 3374, 3721, 4130, 4564, 5011, 5503, 5986, 6531, 7045, 7664, 8273, 8945, 9659, 10383, 11127, 11949, 12809, 13713, 14649, 15633, 16644, 17715, 18735, 19916

Offset: 0

Seiichi Manyama, Jul 17 2024

nonn

Cf. A374707, A374711.

Cf. A034966.

a(n) = my(v=vector(3*n^3+1)); for(i=0, n, for(j=i, n, for(k=j, n, v[i^3+j^3+k^3+1]+=1))); sum(i=1, #v, v[i]>0);

cp's OEIS Frontend

A374707 Number of distinct sums i^3 + j^3 for 0<=i<=j<=n.

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A374714 Number of distinct sums i^3 + j^3 + k^3 + l^3 for 1<=i<=j<=k<=l<=n.

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Python

A374710 Number of distinct sums i^3 + j^3 + k^3 for 0<=i<=j<=k<=n.

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Author

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PARI