A132432 -id:A132432 - cp's OEIS frontend

A225273 T(n,k)=Number of distinct values of the sum of i^2 over n realizations of i in 0..k.

2, 3, 3, 4, 6, 4, 5, 10, 10, 5, 6, 15, 19, 14, 6, 7, 20, 32, 29, 18, 7, 8, 27, 45, 50, 38, 22, 8, 9, 34, 67, 74, 66, 47, 26, 9, 10, 42, 88, 111, 99, 82, 56, 30, 10, 11, 51, 116, 149, 147, 124, 98, 65, 34, 11, 12, 61, 145, 197, 201, 183, 149, 114, 74, 38, 12, 13, 71, 179, 247, 262

Offset: 1

R. H. Hardin May 04 2013

Table starts
..2..3..4...5...6...7...8...9..10..11...12...13...14...15...16...17...18...19
..3..6.10..15..20..27..34..42..51..61...71...83...94..106..120..135..148..165
..4.10.19..32..45..67..88.116.145.179..212..260..300..347..402..464..517..592
..5.14.29..50..74.111.149.197.247.308..370..451..526..613..706..815..914.1037
..6.18.38..66..99.147.201.262.332.411..498..601..702..819..946.1078.1221.1375
..7.22.47..82.124.183.250.326.414.513..621..749..874.1018.1176.1338.1515.1706
..8.26.56..98.149.219.299.390.496.614..742..894.1045.1215.1404.1597.1807.2032
..9.30.65.114.174.255.348.454.577.715..863.1038.1216.1412.1630.1856.2098.2357
.10.34.74.130.199.291.397.518.658.815..984.1182.1385.1608.1855.2114.2388.2681
.11.38.83.146.224.327.446.582.739.915.1105.1326.1554.1804.2080.2370.2677.3005

R. H. Hardin, Table of n, a(n) for n = 1..1325

Row 1 is A000027(n+1)
Row 2 is A047800
Row 3 is A034966
Row 4 is A047801
Row 5 is A132432(n+1)
Row 6 is A132438(n+1)

Empirical: column k is n*k^2 - A225277(k) for large n (n>36 suffices for k through 210)

A132438 Number of different values of i^2+j^2+k^2+l^2+m^2+n^2 for i,j,k,l,m,n in [0,n].

Original entry on oeis.org

1, 7, 22, 47, 82, 124, 183, 250, 326, 414, 513, 621, 749, 874, 1018, 1176, 1338, 1515, 1706, 1899, 2110, 2331, 2568, 2806, 3066, 3324, 3612, 3903, 4201, 4513, 4841, 5173, 5523, 5882, 6248, 6626, 7026, 7433, 7842, 8271, 8715

Offset: 0

Jonathan Vos Post, Nov 13 2007, Nov 14 2007

Number of distinct sums of 6 squares of integers from 0 through n.

			a(1) = 7 because the 7 distinct sums of squares from 0 through 1 are permutations of 1^2 + 1^1 + 1^2 + 1^2 + 1^2 + 1^2 = 6; 1^1 + 1^2 + 1^2 + 1^2 + 1^2 + 0^2 = 5; 1^1 + 1^2 + 1^2 + 1^2 + 0^2 + 0^2 = 4; 1^1 + 1^2 + 1^2 + 0^2 + 0^2 + 0^2 = 3; 1^1 + 1^2 + 0^2 + 0^2 + 0^2 + 0^2 = 2; 1^1 + 0^2 + 0^2 + 0^2 + 0^2 + 0^2 = 1; 0^2 + 0^1 + 0^2 + 0^2 + 0^2 + 0^2 = 0.

Cf. A034966, A047800, A047801, A132432.

Table[Length@ Union@Flatten@ Table[i^2 + j^2 + k^2 + l^2 + m^2 + n^2, {i, 0, p}, {j, i, p}, {k, j, p}, {l, k, p}, {m, l, p}, {n, m, p}], {p, 0, 40}]

Offset corrected by Giovanni Resta, Jun 19 2016

cp's OEIS Frontend

A225273 T(n,k)=Number of distinct values of the sum of i^2 over n realizations of i in 0..k.

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A132438 Number of different values of i^2+j^2+k^2+l^2+m^2+n^2 for i,j,k,l,m,n in [0,n].

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