A225252 T(n,k) = number of distinct values of the sum of n products of two 0..k integers.
2, 4, 3, 7, 8, 4, 10, 16, 12, 5, 15, 27, 25, 16, 6, 19, 42, 43, 34, 20, 7, 26, 59, 67, 59, 43, 24, 8, 31, 81, 95, 92, 75, 52, 28, 9, 37, 105, 130, 131, 117, 91, 61, 32, 10, 43, 134, 169, 179, 167, 142, 107, 70, 36, 11, 54, 167, 215, 233, 228, 203, 167, 123, 79, 40, 12, 60, 203, 267
Offset: 1
Examples
Table starts: ..2..4..7..10..15..19..26..31..37..43...54...60...73...81...90...98..115..124 ..3..8.16..27..42..59..81.105.134.167..203..241..285..331..381..436..495..556 ..4.12.25..43..67..95.130.169.215.267..324..385..454..527..606..692..784..880 ..5.16.34..59..92.131.179.233.296.367..445..529..623..723..831..948.1073.1204 ..6.20.43..75.117.167.228.297.377.467..566..673..792..919.1056.1204.1362.1528 ..7.24.52..91.142.203.277.361.458.567..687..817..961.1115.1281.1460.1651.1852 ..8.28.61.107.167.239.326.425.539.667..808..961.1130.1311.1506.1716.1940.2176 ..9.32.70.123.192.275.375.489.620.767..929.1105.1299.1507.1731.1972.2229.2500 .10.36.79.139.217.311.424.553.701.867.1050.1249.1468.1703.1956.2228.2518.2824 .11.40.88.155.242.347.473.617.782.967.1171.1393.1637.1899.2181.2484.2807.3148
Links
- R. H. Hardin, Table of n, a(n) for n = 1..1325
Formula
Empirical: column k is n*k^2 - A225255(k) for large n (n>2 suffices through k=1000).