A157130 Partial sums of A128201.

1, 4, 8, 13, 20, 29, 40, 53, 68, 84, 101, 120, 141, 164, 189, 216, 245, 276, 309, 344, 380, 417, 456, 497, 540, 585, 632, 681, 732, 785, 840, 897, 956, 1017, 1080, 1144, 1209, 1276, 1345, 1416, 1489, 1564, 1641, 1720, 1801, 1884, 1969, 2056, 2145, 2236, 2329

Offset: 1

Author

Gerald Hillier, Feb 23 2009

Keywords

• nonn

Examples

			First three terms of A128201 are 1, 3, 4, hence a(3) = 1+3+4 = 8.
		

Crossrefs

Cf. A128201 (union of A000290 and A005408), A000290 (squares), A005408 (odd numbers).

Programs

Magma

[(n-r)^2+(4*r^3+6*r^2+2*r)/3 where r is Floor((Sqrt(1+8*n)-1)/4): n in [1..51]];

PARI

{for(n=1, 51, r=floor((sqrt(1+8*n)-1)/4); print1((n-r)^2+(4*r^3+6*r^2+2*r)/3, ","))}

Formula

a(n) = (n-r)^2+(4*r^3+6*r^2+2*r)/3 where r = floor((sqrt(1+8*n)-1)/4). - Simplified by Gerald Hillier, Apr 14 2015

Extensions

Edited and extended by Klaus Brockhaus, Feb 24 2009