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

1,2

Links

Table of n, a(n) for n=1..51.

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

Example

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

Prog

(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, ", "))}

Crossrefs

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

Sequence in context: A362016 A071994 A023661 * A172050 A312219 A312220

Adjacent sequences: A157127 A157128 A157129 * A157131 A157132 A157133

Keyword

nonn

Author

Gerald Hillier, Feb 23 2009

Extensions

Edited and extended by Klaus Brockhaus, Feb 24 2009

Status

approved